Optimal Sensor Placement Research Articles

Complexity of spatio-temporal plantar pressure patterns during everyday behaviours.

The human foot sole is the primary interface with the external world during balance and walking, and also provides important tactile information on the state of contact. However, prior studies on plantar pressure have focused mostly on summary metrics such as overall force or centre of pressure under limited conditions. Here, we recorded spatio-temporal plantar pressure patterns with high spatial resolution while participants completed a wide range of daily activities, including balancing, locomotion and jumping tasks. Contact area differed across task categories, but was only moderately correlated with the overall force experienced by the foot sole. The centre of pressure was often located outside the contact area or in locations experiencing relatively low pressure, and therefore a result of disparate contact regions spread widely across the foot. Non-negative matrix factorization revealed low-dimensional spatial complexity that increased during interaction with unstable surfaces. Additionally, pressure patterns at the heel and metatarsals decomposed into separately located and robustly identifiable components, jointly capturing most variance in the signal. These results suggest optimal sensor placements to capture task-relevant spatial information and provide insight into how pressure varies spatially on the foot sole during a wide variety of natural behaviours.

Bayesian optimal sensor placement for parameter estimation under modeling and input uncertainties

A Bayesian optimal sensor placement (OSP) framework for parameter estimation in nonlinear structural dynamics models is proposed, based on maximizing a utility function built from appropriate measures of information contained in the input–output response time history data. The information gain is quantified using Kullback–Leibler divergence (KL-div) between the prior and posterior distribution of the model parameters. The design variables may include the type and location of sensors. Asymptotic approximations, valid for large number of data, provide valuable insight into the measure of information. Robustness to uncertainties in nuisance (non-updatable) parameters associated with modeling and excitation uncertainties is considered by maximizing the expected information gain over all possible values of the nuisance parameters. In particular, the framework handles the case where the excitation time history is measured by installed sensors but remains unknown at the experimental design phase. Introducing stochastic excitation models, the expected information gain is taken over the large number of uncertain parameters used to model the random variability in the input time histories. Monte Carlo or sparse grid methods estimate the multidimensional probability integrals arising in the formulation. Heuristic algorithms are used to solve the optimization problem. The effectiveness of the method is demonstrated for a multi-degree of freedom (DOF) spring–mass chain system with restoring elements that exhibit hysteretic nonlinearities.

Development of Active Noise Control System Optimized for Road Noise Reduction

In this paper, a newly developed Active Noise Control (ANC) system is introduced, that effectively reduces road noise, which becomes a major issue with electrified vehicles, and that enhances vehicle interior sound levels matching seamless acceleration by electric drive. Conventionally, reducing road noise using ANC requires numerous sensors and speakers, as well as a processor with high computing power. Therefore, the increase in system cost and the complexity of the system are obstacles to its spread. To overcome these issues, this system is developed based on four concepts. The first is a modular system configuration with unified interface to apply to various vehicle types and grades. The second is the integration and optimal placement of noise source reference sensors to achieve both reduction in number of parts and noise reduction performance. The third is the application of digital communications that combine power superposition, low latency, and high throughput to reduce wiring. The fourth is the development of control technologies that specialize in in-vehicle acoustic characteristics to achieve both computational efficiency and noise reduction performance. The one is a technology to integrate control paths based on the sound field mode characteristics in the vehicle cabin, and another one is the frequency band restrain control technology that matches speaker output characteristics. It is confirmed that this proposed system achieves quietness improvement equivalent to the difference of vehicle segmentation with a minimum system configuration, and that this system has a high superiority in weight efficiency compared to conventional vehicle body measures.

Neural-Inspired Measurement Observability

The neural encoding by biological sensors of flying insects, which prefilters stimulus data before sending them to the central nervous system in the form of voltage spikes, enables sensing capabilities that are computationally low cost while also being highly robust to noise. This process, which can be modeled as the composition of a linear moving average filter and a nonlinear decision function, inspired the work reported here to improve engineered sensing performance by maximizing the observability of particular neural-inspired composite measurement functions. We first present a tool to determine the observability of a linear system with measurement delay (the first element of the composition), and then use a Lie algebraic observability approach to study nonlinear autonomous systems with output delay (the second element of the composition). The Lie algebraic tools are then extended to address overall observability of systems with composite outputs as in the neural encoder model we adopt. The analytical outcomes are supported using the empirical observability Gramian, and optimal sensor placement on a bioinspired wing model is performed using metrics based on the empirical Gramian.

A sensitivity-based approach to optimal sensor selection for complex processes

Sensor selection is critical for state estimation, control and monitoring of nonlinear processes. However, it is impractical to evaluate the performance of all the combinations of the potentially available sensors using exhaustive search unless the sensor set is small. In this paper, we present a sensitivity-based approach for determining the minimum number of sensors and their optimal locations for state estimation. The observability is measured using the local sensitivity matrix of the output measurements to initial states. Based on this matrix, we determine the minimum number of sensors required to achieve full column rank. The optimal sensor placement is thought to be the sensor set that provides the maximum degree of observability among all sets that meet the full-rank requirement. The computational complexity of sensor selection is significantly reduced by successive orthogonalization of the columns of the sensitivity matrix. To validate the effectiveness of the proposed method, it is applied to two processes: four continuous stirred-tank reactors and a wastewater treatment plant. In both cases, the proposed approach can obtain the optimal sensor subset.

Gaussian mixture models for the optimal sparse sampling of offshore wind resource

Abstract. Wind resource assessment is a crucial step for the development of offshore wind energy. It relies on the installation of measurement devices, whose placement is an open challenge for developers. Indeed, the optimal sensor placement for field reconstruction is an open challenge in the field of sparse sampling. As for the application to offshore wind field reconstruction, no similar study was found, and standard strategies are based on semi-empirical choices. In this paper, a sparse sampling method using a Gaussian mixture model on numerical weather prediction data is developed for offshore wind reconstruction. It is applied to France's main offshore wind energy development areas: Normandy, southern Brittany and the Mediterranean Sea. The study is based on 3 years of Météo-France AROME's data, available through the MeteoNet data set. Using a Gaussian mixture model for data clustering, it leads to optimal sensor locations with regards to wind field reconstruction error. The proposed workflow is described and compared to state-of-the-art methods for sparse sampling. It constitutes a robust yet simple method for the definition of optimal sensor siting for offshore wind field reconstruction. The described method applied to the study area output sensor arrays of respectively seven, four and four sensors for Normandy, southern Brittany and the Mediterranean Sea. Those sensor arrays perform approximately 20 % better than the median Monte Carlo case and more than 30 % better than state-of-the-art methods with regards to wind field reconstruction error.

Performance-based optimal sensor placement method for single-layer reticulated shells considering modal observability and damage identifiability

Structural health monitoring allows for the early detection of structural damage and provide valuable insight into structural performance. However, duo to numerous degrees of freedom and dense vibration modals, designing a sensor placement scheme for Single-Layer Reticulated Shells (SLRSs) is a challenging task. This paper introduces two performance indexes, namely the modal observability and damage identifiability, to quantitatively evaluate the efficiency of the sensor system. Subsequently, based on these indexes, the multi-objective optimization algorithm, as well as the performance-based design concepts, a novel performance-based optimal sensor placement (OSP) method for SLRSs is proposed. Two types of sensor placement performance curves, namely the sensor placement effect curve and the sensor placement proportion curve, are presented to determine the optimal number and placement of sensors in different directions. Numerical examples demonstrate that the proposed method can generate OSP schemes that meet various performance targets, and the performance-based OSP method is superior to the simple multi-objective OSP method. Furthermore, suggestion on selecting the total number of sensors for practical engineering applications is also provided.

Two-timescale stochastic gradient descent in continuous time with applications to joint online parameter estimation and optimal sensor placement

In this paper, we establish the almost sure convergence of two-timescale stochastic gradient descent algorithms in continuous time under general noise and stability conditions, extending well known results in discrete time. We analyse algorithms with additive noise and those with non-additive noise. In the non-additive case, our analysis is carried out under the assumption that the noise is a continuous-time Markov process, controlled by the algorithm states. The algorithms we consider can be applied to a broad class of bilevel optimisation problems. We study one such problem in detail, namely, the problem of joint online parameter estimation and optimal sensor placement for a partially observed diffusion process. We demonstrate how this can be formulated as a bilevel optimisation problem, and propose a solution in the form of a continuous-time, two-timescale, stochastic gradient descent algorithm. Furthermore, under suitable conditions on the latent signal, the filter, and the filter derivatives, we establish almost sure convergence of the online parameter estimates and optimal sensor placements to the stationary points of the asymptotic log-likelihood and asymptotic filter covariance, respectively. We also provide numerical examples, illustrating the application of the proposed methodology to a partially observed Beneš equation, and a partially observed stochastic advection-diffusion equation.

Optimal Sensor Placement via Parameterized Background Data Weak Method Applied to Magnetostatic Problems Including Anisotropy

The need for electrical machines is growing in a wide range of applications nowadays, such as for energy production, automotive, marine, and medical equipment, etc. The reliability, efficiency, performance and operational safety are always critical issues, which implies that the monitoring and analysis during the operation of the equipment need to be strengthened. In general, more sensors can give higher accuracy of the estimated physical quantity, but bring a more expensive cost. To address this issue, an algorithm principally based on the parameterized background data-weak (PBDW) method is proposed and adopted in this work to optimize both the number and the location of sensors. Besides, to further investigate the performance of the proposed algorithm, a prototype concerning an anisotropic magnetostatic problem is studied as an example for the placement of magnetic sensors. The numerical experiments shows that the proposed method can achieve very satisfactory results in different aspects.

Merging experimental design and structural identification around the concept of modified Constitutive Relation Error in low-frequency dynamics for enhanced structural monitoring

This paper presents a novel Optimal Sensor Placement (OSP) strategy that is dedicated to model updating problems based on the modified Constitutive Relation Error (mCRE) functional in low-frequency dynamics. The mCRE is a credible alternative to model updating functionals that stands out by searching structural parameters alongside mechanical fields as the best trade-off between all available information from measured data, without any further a priori assumption. Considering damage detection problems, due to possible discrepancies in terms of parameters sensitivity with respect to mCRE, sensor locations provided by standard OSP algorithms may be irrelevant. The proposed approach uses the concept of Information Entropy by formulating a modified Fisher information matrix, in which the sensitivity of the mCRE mechanical fields with respect to the updated parameters is involved. The approach is legitimated by the strong connection between mCRE and Bayesian inference. A proof-of-concept involving an earthquake engineering inspired academic case study, where accelerometers are positioned on a two-story frame structure subjected to random ground motion, permits to illustrate the soundness and efficiency of the proposed methodology compared to other classical OSP techniques. The influence of critical mCRE parameters is shown, as well as the benefits of taking multiple scenarios into account so as to get an OSP that is relevant for a wider range of possible damage occurrences.

Multi-objective acoustic sensor placement optimization for crack detection of compressor blade based on reinforcement learning

Nowadays, acoustic sensors have been widely applied for structural health monitoring and crack detection of compressor blades. As the detection accuracy is mainly affected by signal quality, the optimal sensor placement (OSP) is significant for crack detection. To search the OSP for reliable signals, the multi-objective acoustic sensor placement optimization method is proposed based on information field fitting and optimization with reinforcement learning. First, the improved ridge and least squares support vector regression (R-LS-SVR) method is presented to fit information field of acoustic signal. Besides, the multi-objective function is constructed based on the compressor operation conditions, sound quality and crack damage observation. In addition, the Pareto front is obtained to realize multi-objective optimization (MOO) based on non-dominated sorting genetic algorithms (NSGA-II). Furtherly, the reinforcement learning-based pattern search method (RL-PSM) is proposed to quickly search the OSP of acoustic sensor. The compressor experiments are implemented to test the proposed method, and it can detect crack with the accuracy of 99.17%, which is superior to other locations. Comparing with other fitting and optimization methods, the advantage of the proposed method is validated for OSP optimization and crack detection.

Multiobjective-clustering-based optimal heterogeneous sensor placement method for thermo-mechanical load identification

The direct measurement of external loads acting on structures remains a challenge in many engineering applications. In this context, mechanical load identification has received considerable attention to inverse them using some response signals. Obviously, sensor placement is fundamental to the success of load identification. Considering temperature effects in the environment, this study investigates an optimal heterogeneous sensor placement framework for multi-case mechanical load identification. Firstly, the temperature field approximation method is developed using the measuring points with the minimum error in RBF interpolation. Based on the modal superposition theory, the formulas of mechanical load identification under static and dynamic cases are then deduced utilizing the responses eliminating thermal-oriented components. With the specific loading position, an index of the modal contribution rate is defined to provide a reasonable modal selection. Further, an optimal placement framework of multi-type response sensors (strain gauges and accelerometers) considering distance constraints is constructed for mechanical load identification under static/dynamic multiple cases, in which the optimization objective integrates the global performance and local evaluation of the interested modal loads. More specifically, an algorithm of collaborative clustering for heterogeneous modal matrices is involved to avoid redundant information and alleviate the computation burden. Eventually, two numerical examples are discussed to demonstrate the validity and feasibility of the developed approach.

Optimal sensor placement methodology of triaxial accelerometers using combined metaheuristic algorithms for structural health monitoring applications

Structural health monitoring applications present a valuable opportunity for cities to improve their infrastructures environmental life cycle, reduce operational maintenance cost and enhance their resiliency through early damage detection capabilities. The dilemma with structural health monitoring resides in balancing between the number of sensors to be installed and the amount of data that needs to be transferred, stored, and managed. These technical complications directly impact the cost efficiency of such solutions. Thus, limiting the wide range deployment of such technology. Henceforth, Optimal Sensor Placement (OSP) methodologies offers the possibility to optimize the sensor configuration that will ensure a proper and cost-efficient monitoring system to obtain the maximum modal information related to any infrastructure type.In this study, a novel “Modal Assurance Criterion (MAC)”-based methodology with the aim of the optimal sensor placement is presented using a 410 m high rise structure. The Modal Kinetic Energy (MKE) and a MAC-based objective function are combined in the suggested methodology. The optimization problem is solved using a new hybrid metaheuristic algorithm that combines Teaching–Learning-Based Optimization (TLBO), Artificial Bee Colonies (ABC), and Stochastic Paint Optimizer (SPO). With no user-defined parameters, the combination of algorithms exhibits up to 86% better fitness, avoids local optimums due to higher accuracy, and shows promising results for cost calculation optimization because it requires 50% to 70% fewer iterations compared to six evolutionary algorithms that are usually used.

A new convolutional neural network-based framework and data construction method for structural damage identification considering sensor placement

In the application of data driven structural damage identification (SDI) based on supervised deep learning technology, valid data demarcation is the foundation; a convolutional neural network model with learning ability and capability of processing rich signal information is the core. Based on this understanding, this work makes three contributions: Firstly, the structural damage location and severity are jointly demarcated, and the SDI problem is transformed into a multi-classification task. Secondly, a 3D signal processing convolutional neural networks (3DS-CNN) is designed with an attempt to identify the complex and slight damages using the most basic network structure. Thirdly, a ‘major and subsidiary’ data construction (MSDC) method integrating the key intrinsic mode function is proposed to construct 3D data. Then the proposed schemes are verified by two different structures. The results show that the 3DS-CNN has excellent damage identification ability for small-size data with noise pollution. MSDC method can enrich the feature information of the damage signals and help the network with deep feature excavation, even if the vibration signals are heavily polluted. Going one step further, the impact of sensor placement is discussed, and it is found that when external excitation is obvious, better SDI accuracy can be achieved even using a single sensor signal with slight noise. When the noise interference is obvious, the generalization ability and noise robustness of the network can be enhanced by optimizing sensor placement. In this case, the sensor placement criteria and the sensitive nodes of the structure should be comprehensively and carefully considered to avoid mutual ‘coupling’ interference of data between sensors.

Predicting Ventilation Rate in a Naturally Ventilated Dairy Barn in Wind-Forced Conditions Using Machine Learning Techniques

Precise ventilation rate estimation of a naturally ventilated livestock building can benefit the control of the indoor environment. Machine learning has become a useful technique in many research fields and might be applied to ventilation rate prediction. This paper developed a machine-learning model for ventilation rate prediction from batch computational fluid dynamics (CFD) simulation results. By comparing deep neural networks (DNN), support vector regression (SVR), and random forest (RF), the best machine learning algorithm was selected. By comparing the modeling scheme of direct single-output (ventilation rate) and indirect multiple-output (predict averaged air velocities normal to the openings, then calculate the ventilation rate), the performances of the machine learning models widely applied in ventilation rate prediction were evaluated. In addition, this paper further evaluated the impact of adding indoor air velocity measurement in ventilation rate prediction. The results showed that the modeling performance of the DNN algorithm (Mean Absolute Percentage Error (MAPE) = 20.1%) was better than those of the SVR (MAPE = 23.2%) and RF algorithm (MAPE = 21.0%). The scheme of multiple-output performed better (MAPE < 8%) than the single-output scheme (MAPE = 20.1%), where MAPE was the mean absolute percentage error. Additionally, the comparison of modeling schemes with different inputs showed that the predictive accuracy could be improved by adding indoor velocities to the inputs. The MAPE decreased from 7.7% in the scheme without indoor velocity to 4.4% in the scheme with one indoor velocity, and 3.1% in the scheme with two indoor velocities. The location of the additional air velocity affected the accuracy of the predictive model, with the ones at the bottom layer performing better in the prediction than those at the top layer. This study enables a real-time and accurate prediction of the ventilation rate of a barn and provides a recommendation for optimal indoor sensor placement.

A new optimal sensor placement method for virtual sensing of composite laminate

Identifying modal coordinates from output-only data is a key link of virtual sensing technology based on the modal extension method. It is also one of the goals of optimal sensor placement (OSP). Traditional OSP methods are based on the underlying assumption that the estimated values of modal coordinates are unbiased estimates of real values. However, due to uncertainty and the characteristics of an inverse problem, the unbiased estimation obtained from the output-only data may seriously deviate from the true value. This study proposes a new OSP method for composite virtual strain sensing, which can obtain the global unbiased estimation of modal coordinates. First, a Bayesian probabilistic model for virtual sensing considering model uncertainty and measurement error is formulated. Then, the K-L divergence, which measures the reduction in utility by removing sensors from the full configuration, is used to obtain the unbiased estimation of modal parameters. Finally, using the regularization mechanism in the Bayesian method, a new variance determination method is proposed to improve the stability of the solution. Considering both unbiasedness and stability, NSGA-II multi-objective optimization algorithm and two OSP evaluation criteria are used to obtain the final optimal sensor placement. To illustrate the effectiveness of the proposed method, an example involving a laminate plate is considered, accompanied by comprehensive discussions.

Reconstruction of full-field dynamic responses for large-scale structures using optimal sensor placement

This study explores an optimal sensor placement approach for reconstructing full-field dynamic responses using a set of basic vectors obtained from high-fidelity data. The novelty is the combination of the reduced-order model with sparse promotion, which makes the sensor optimization algorithm effective. Pivoted QR decomposition was performed to accelerate the full-field reconstruction of large-scale structures. To improve the reconstruction precision, an online–offline paradigm was used to create the reduced-order model offline and estimate the sparse coefficient online. The proposed method was verified using a high-rise building case study. The influential factors of reconstruction precision, such as measurement noise, different mode orders, number of sensors, and various types of dynamic responses, were investigated. The results show that the proposed method is accurate and reliable for reconstructing full-field responses, providing a potential alternative for structural health monitoring of large-scale structures.

Connection fault diagnosis for lithium-ion battery packs in electric vehicles based on mechanical vibration signals and broad belief network

The connection faults between the cells of a battery pack can increase contact resistance and thus result in abnormal heating at the connections, which can seriously damage or even fail the battery pack. This work therefore proposes a novel connection fault diagnosis method based on mechanical vibration signals rather than voltage and current measurements. Firstly, this work simulates the vibration environment, which resembles that of the actual operation of a lithium-ion battery pack in electric vehicles. The optimal sensor placement is achieved via a sparse-learning algorithm, and the vibration signals are collected on this basis. Following that, this work proposes a broad belief network (BBN) for detecting and locating connection faults in lithium-ion battery packs based on the vibration signals. Since fault diagnosis needs to adapt to new data as they become progressively available in real-time, two incremental-learning algorithms are paired with the BBN, such that the network can achieve fast reconstruction and expansion without re-training from scratch. Empirical evidence suggests that the diagnostic accuracy of the proposed method is 93.25%, which demonstrates the effectiveness and feasibility of the proposed method.

A data-driven sensor placement strategy for reconstruction of mode shapes by using recurrent Gaussian process regression

Current Optimal Sensor Placement (OSP) strategies for bridges mostly rely on data from a finite element model rather than from the real structure due to high cost in placing massive sensors for data collection. For large-scale bridges, however, it is difficult to formulate a precise model and thus the OSP strategies building upon a finite element model inevitably suffer from modelling errors. Besides, the finite element model cannot account for real measurement noise. Premised on the fact that it is not expensive to make in-situ trial measurements with a few sensors on a target bridge before deploying a structural health monitoring (SHM) system on it, a data-driven OSP strategy is proposed in this study which aims at accurately reconstructing mode shapes (to facilitate vibration-based structural damage detection) by using only a few vibration sensors to be included in the SHM system. The proposed OSP strategy is also applicable for the upgrade of a long-term SHM system currently deployed on a bridge, by using historical data collected from the current SHM system. To precisely reconstruct mode shapes, a two-stage OSP strategy in terms of Recurrent Gaussian Process Regression (RGPR) is developed, and its performance is validated on a simulation model and a real bridge. In the first stage, the greedy algorithm is leveraged to temporarily deploy sensors on the structure and train accurate RGPR models using the collected data, which are used to afford spatially complete mode shape data for optimization later. Starting from a few sensors temporarily deployed on the bridge, a one-by-one sensor adding procedure is performed to configure increasing sensors until the target is achieved. In the second stage, Cuckoo Search (CS) algorithm is pursued to obtain the globally optimal sensor placement solution, from which the temporarily deployed sensors can be re-configured to the optimum positions. Both the best sensor quantity and positions are obtained by the proposed OSP strategy.

A review of the application of the simulated annealing algorithm in structural health monitoring (1995-2021)

In recent years, many innovative optimization algorithms have been developed. These algorithms have been employed to solve structural damage detection problems as an inverse solution. However, traditional optimization methods such as particle swarm optimization, simulated annealing (SA), and genetic algorithm are constantly employed to detect damages in the structures. This paper reviews the application of SA in different disciplines of structural health monitoring, such as damage detection, finite element model updating, optimal sensor placement, and system identification. The methodologies, objectives, and results of publications conducted between 1995 and 2021 are analyzed. This paper also provides an in-depth discussion of different open questions and research directions in this area.