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Fault isolation and sensor placement are vital for monitoring and diagnosis. A sensor conveys information about a system's state that guides troubleshooting if problems arise. We are using machine learning methods to uncover behavioral patterns over snapshots of system simulations that will aid fault isolation and sensor placement, with an eye towards minimality, fault coverage, and noise tolerance.
An approach is presented to evaluating sensor placements to maximize monitorability of the target system while minimizing the number of sensors. The approach uses a model of the monitored system to score potential sensor placements on the basis of four monitorability criteria. The scores can then be analyzed to produce a recommended sensor set. An example from our NASA application domain is used to illustrate our model-based approach to sensor placement.
There are multiple different algorithms to perform modal test sensor placement optimization: effective independence, residual kinetic energy, iterative Guyan reduction, genetic algorithms, or a brute-force methodology. However, any of these methods may be computationally expensive, especially for structural models with a large number of degrees of freedom. Given the high-cost and the need to optimize the solution, modal sensor placement is a great application for machine learning (ML) algorithms. In this paper, we will apply ML algorithms to determine the optimal sensor locations for simple and complex structures. We will also discuss the benefits and drawbacks of using machine learning over other sensor placement algorithms.
This paper presents an approach to evaluating sensor placements on the basis of how well they are able to discriminate between a given fault and normal operating modes and/or other fault modes. In this approach, a model of the system in both normal operations and fault modes is used to evaluate possible sensor placements upon the basis of three criteria. Discriminability measures how much of a divergence in expected sensor readings the two system modes can be expected to produce. Accuracy measures confidence in the particular model predictions. Timeliness measures how long after the fault occurrence the expected divergence will take place. These three metrics then can be used to form a recommendation for a sensor placement. This paper describes how these measures can be computed and illustrated these methods with a brief example.
The problem of selecting optimal locations of actuators and sensors for the control of flexible structures is addressed. Novel geometrical and physical interpretations are given for both controllability and observability grammians which enhances the intuitive aspects of the actuator and sensor placement problem. The explicit form of controllability and observability grammians for flexible structures is used to define modal grammian coefficients, which provides the basis for an actuator and sensor placement technique. The relationship of the proposed metric to three different existing criteria are given. The method is demonstrated on a model of an experimental large flexible structure.
Nuclear power plants (NPPs) require continuous monitoring of various systems, structures, and components to ensure safe and efficient operations. The critical safety testing of new fuel compositions and the analysis of the effects of power transients on core temperatures can be achieved through modeling and simulations. They capture the dynamics of the physical phenomenon associated with failure modes and facilitate the creation of digital twins (DTs). Accurate reconstruction of fields of interest (e.g., temperature, pressure, velocity) from sensor measurements is crucial to establish a two-way communication between physical experiments and models. Sensor placement is highly constrained in most nuclear subsystems due to challenging operating conditions and inherent spatial limitations. This study develops optimized data-driven sensor placements for full-field reconstruction within reactor and steam generator subsystems of NPPs. Optimized constrained sensors reconstruct field of interest within a tri-structural isotropic (TRISO) fuel irradiation experiment, a lumped parameter model of a nuclear fuel test rod and a steam generator. The optimization procedure leverages reduced-order models of flow physics to provide a highly accurate full-field reconstruction of responses of interest, noise-induced uncertainty quantification and physically feasible sensor locations. Accurate sensor-based reconstructions establish a foundation for the digital twinning of subsystems, culminating in a comprehensive DT aggregate of an NPP.
This paper examines the sensitivity of experimentally measured modal frequencies and mode shapes to structural reassembly and sensor placement errors on a suspended three-bay truss. The statistical variations of identified mode shapes and frequencies are measured by repeated experiments. Both parameters are shown to vary measurably more with reassembly than sensor placement errors. Also, a directional stiffness in the truss joints was found to cause a parameter dependence on member orientation during reconstruction.
Systems health management, and in particular fault diagnosis, is important for ensuring safe, correct, and efficient operation of complex engineering systems. The performance of an online health monitoring system depends critically on the available sensors of the system. However, the set of selected sensors is subject to many constraints, such as cost and weight, and hence, these sensors must be selected judiciously. This paper presents an offline design-time sensor placement approach for complex systems. Our diagnosis method is built upon the analysis of model-based residuals, which are computed using structural model decomposition. Sensor placement in this framework manifests as a residual selection problem, and we aim to find the set of residuals that achieves single-fault diagnosability of the system, uses the minimum number of sensors, and corresponds to the best model decomposition for the best distribution of the diagnosis system. We present a set of algorithms for solving this problem and compare their performance in terms of computational complexity and optimality of solutions. We demonstrate the approach using a benchmark multi-tank system.
Stochastic fluctuations in power injections from distributed energy resources (DERs) combined with load variability can cause constraint violations (e.g., exceeded voltage limits) in electric distribution systems. To monitor grid operations, sensors are placed to measure important quantities such as the voltage magnitudes. Here, in this paper, we consider a sensor placement problem which seeks to identify locations for installing sensors that can capture all possible violations of voltage magnitude limits. We formulate a bilevel optimization problem that minimizes the number of sensors and avoids false sensor alarms in the upper level while ensuring detection of any voltage violations in the lower level. This problem is challenging due to the nonlinearity of the power flow equations and the presence of binary variables. Accordingly, we employ recently developed conservative linear approximations of the power flow equations that overestimate or underestimate the voltage magnitudes. By replacing the nonlinear power flow equations with conservative linear approximations, we can ensure that the resulting sensor locations and thresholds are sufficient to identify any constraint violations. Additionally, we apply various problem reformulations to significantly improve computational tractability while simultaneously ensuring an appropriate placement of sensors. Lastly, we improve the quality of the results via an approximate gradient descent method that adjusts the sensor thresholds. We demonstrate the effectiveness of our proposed method for several test cases, including a system with multiple switching configurations.
Previous research into object localization has shown that sensor placement and alignment plays an important role in achieving higher accuracy levels of the estimated location of a tracked Urban Air Mobility Vehicle. In general, a near-orthogonal intersection between the ground node observation vectors results in the highest accuracy due to a smaller overlapping uncertainty region between both. This applies to triangulation by means of ground node camera angle observations as well as trilateration by means of ground node distance measurements. However, this simple concept is not easily fulfilled with a network of a limited number of static ground nodes and a moving object to be localized. This case study performs sensitivity analyses and explores practical ways on how to achieve higher estimate accuracy levels in this context.
Previous research into object localization has shown that sensor placement and alignment plays an important role in achieving higher accuracy levels of the estimated location of a tracked Urban Air Mobility Vehicle. In general, a near-orthogonal intersection between the ground node observation vectors results in the highest accuracy due to a smaller overlapping uncertainty region between both. This applies to triangulation by means of ground node camera angle observations as well as trilateration by means of ground node distance measurements. However, this simple concept is not easily fulfilled with a network of a limited number of static ground nodes and a moving object to be localized. This case study performs sensitivity analyses and explores practical ways on how to achieve higher estimate accuracy levels in this context.
Optimal design of experiments for Bayesian inverse problems has recently gained wide popularity and attracted much attention, especially in the computational science and Bayesian inversion communities. An optimal design maximizes a predefined utility function that is formulated in terms of the elements of an inverse problem, an example being optimal sensor placement for parameter identification. The state-of-the-art algorithmic approaches following this simple formulation generally overlook misspecification of the elements of the inverse problem, such as the prior or the measurement uncertainties. This work presents an efficient algorithmic approach for designing optimal experimental design schemes for Bayesian linear inverse problems such that the optimal design is robust to misspecification of elements of the inverse problem. Specifically, we consider a worst-case scenario approach for the uncertain or misspecified parameters, formulate robust objectives, and propose an algorithmic approach for optimizing such objectives. Furthermore, both relaxation and stochastic solution approaches are discussed with detailed analysis and insight into the interpretation of the problem and the proposed algorithmic approach. Extensive numerical experiments to validate and analyze the proposed approach are carried out for sensor placement in a parameter identification problem.
For various reasons as discussed for instance in, the selection of actuator and sensor positions is still ad hoc. This is especially true for flexible structures where many candidate configurations can exist. This study is an attempt to make the selection process more methodical. One approach to actuator and sensor placement is to optimize a closed loop performance metric directly by selecting the actuators, sensors, and controller gains simultaneously. This direct approach makes sense if the desired closed loop performance is well defined. Since the individual actuator and sensor contributions to the closed loop performance metric is complex, the solution strategy usually employs non linear programming with many design and numerical iterations. A second approach is to select actuators and/or sensors based on open loop properties so that closed loop performance is indirectly optimized. Since the individual sensor and actuator contributions to the open loop metric is simple, nonlinear optimization is usually not needed. This approach will suggest efficient actuator and sensor configurations for any type of control law. The method suggested in this study falls into the latter class of approaches.
A new approach based on the steady-state solutions of the optimal control and estimation problems is presented to study respectively the actuator and sensor locations for large flexible structures. A simple and computer-implementable formulation for minimizing the steady state optimal cost function and the state estimation error inherent in the estimation process is given. In conjunction with the new approach, two criteria are established relating the actuator and the sensor placement optimalities respectively to the minimums of the optimal cost function and the state estimation error. To illustrate the concepts of this paper, we present the results of some numerical and analytical studies on the actuator and the sensor locations of several simple flexible beam modes.
Anticipating the construction of the international space station, on-orbit modal identification of space platforms through optimally placed accelerometers is an area of recent activity. Unwanted vibrations in the platform could affect the results of experiments which are planned. Therefore, it is important that sensors (accelerometers) be strategically placed to identify the amount and extent of these unwanted vibrations, and to validate the mathematical models used to predict the loads and dynamic response. Due to cost, installation, and data management issues, only a limited number of sensors will be available for placement. This work evaluates and compares four representative sensor placement algorithms for modal identification. Most of the sensor placement work to date has employed only numerical simulations for comparison. This work uses experimental data from a fully-instrumented truss structure which was one of a series of structures designed for research in dynamic scale model ground testing of large space structures at NASA Langley Research Center. Results from this comparison show that for this cantilevered structure, the algorithm based on Guyan reduction is rated slightly better than that based on Effective Independence.
Systems of fixed-position radiation sensors can provide information that assists emergency responders following nuclear and radiological incidents. State, local, tribal, and territorial (SLTT) government agencies that implement systems of fixed-position sensors are faced with numerous decisions regarding sensor selection, quantity, and placement. To develop guidance on implementation of radiation detection systems, we simulated the release of radioactive material in an urban environment using a combination of three models: the Weather Research Forecasting (WRF), Quick Urban and Industrial Complex (QUIC), and Monte Carlo N-Particle (MCNP) models. We then evaluated the performance of several hypothetical sensor systems. The small number of simulations we conducted are not sufficient to generate definitive design guidance for radiation sensor systems, but we did identify trends that would be of interest to emergency planners. For a scenario that releases 1000 curies of Cs-137, radiation detectors were needed at 500-meter intervals to have a high likelihood of event detection and to estimate source location and plume detection. We also noted that optimal detector altitude varied with distance to the source. We recommend additional research in this area be conducted to support developing sensor placement guidelines that expand on a range of locations, isotopes, activity levels, and different weather conditions. Original simulation strategies included a range of environments, additional radioisotopes (Am241 and AmBe), and a larger selection of sensor types. These types of expansions would support SLTT guidance on sensor system recommendations.
Systems of fixed-position radiation sensors can provide information that assists emergency responders following nuclear incidents. First responder organizations that implement systems of fixed-position sensors face numerous decisions regarding sensor selection, quantity, and placement. Researchers at Pacific Northwest National Laboratory (PNNL) have evaluated the performance of several hypothetical sensor systems during a simulated activation of a radiological dispersal device. Due to technical limitations, PNNL’s analysis was limited to a single location and number of scenarios. This document describes additional research and analysis that would result in improved guidance to first responder organizations considering installation of radiation monitoring systems.
There has been considerable research on choosing actuator and sensor locations in large flexible spacecraft in order to optimize the controllability and observability of the system, or to maximize some objective function of control system performance. Future large flexible spacecraft may require on-orbit identification of the structure to tune the control system, because such tests cannot be performed in a one-g environment before launch. This indicates that the choice of actuator and sensor locations must serve a dual purpose, for control and for identification. This paper develops concepts for a degree of identifiability and studies placement of actuators and sensors on a free-free beam to optimize such objective functions. The results in this simple situation suggest that in free-free spacecraft structures in orbit, placement for control and placement for identification may often be consistent objectives rather than conflicting objectives.