“…Spatial problems, e.g. [16]- [20], on the other hand, consist of an array of sensors. The advent of CPS is supporting the proliferation of such multisensor measurement systems; whereby the distributed sensordata is synchronously sampled and then collected at various computing nodes.…”
Section: A Temporal and Spatial Inverse Problemsmentioning
This paper presents a new matrix algebraic approach to the direct solution of inverse boundary value problems (IBVP). The synthesis of admissible functions and differentiating matrices is given particular attention. All the necessary mathematical elements are derived from basic principles. The method yields a linear operator for the solution of IBVPs. A single matrix multiplication is required at run-time to determine the solution. The number of FLOPS required is constant and known apriory making the solution suitable for use in embedded realtime systems. The concept of discrete basis function design is introduced for the first time. The method enables the design of special discrete basis functions which yield optimal noise performance and numerical efficiency for specific tasks. All the methods are also verified in a laboratory test system and compared with results from an optical reference measurement.
“…Spatial problems, e.g. [16]- [20], on the other hand, consist of an array of sensors. The advent of CPS is supporting the proliferation of such multisensor measurement systems; whereby the distributed sensordata is synchronously sampled and then collected at various computing nodes.…”
Section: A Temporal and Spatial Inverse Problemsmentioning
This paper presents a new matrix algebraic approach to the direct solution of inverse boundary value problems (IBVP). The synthesis of admissible functions and differentiating matrices is given particular attention. All the necessary mathematical elements are derived from basic principles. The method yields a linear operator for the solution of IBVPs. A single matrix multiplication is required at run-time to determine the solution. The number of FLOPS required is constant and known apriory making the solution suitable for use in embedded realtime systems. The concept of discrete basis function design is introduced for the first time. The method enables the design of special discrete basis functions which yield optimal noise performance and numerical efficiency for specific tasks. All the methods are also verified in a laboratory test system and compared with results from an optical reference measurement.
“…A good overview of applications can be found in Machan and Bennett [4]. Further applications, in the monitoring of rigid structures, can be found in [5] [7]. None of the cited literature deals with the solution of over constrained systems or with the computation of the confidence interval associated with perturbations.…”
This paper presents the theoretical back ground for a new measurement system for the monitoring of possible road subsidence and its verification with exper imental results. A combination of theodolite measurements and inclinometers are used to perform the monitoring of possible land subsidence. The aim is to detect ground motion near critical infrastructure during excavation is the vicinity. The required computation corresponds to an inverse boundary value problem with uncertain boundary values. The solution is formulated as a covariance weighted Hermite approximation problem. Additionally, a method of taking advantage of the properties of the over-constrained system to identify a defective sensor is presented. The correct functionality of the proposed method and its performance in terms of uncertainty is demonstrated with a Monte Carlo simulation. Additionally, tests were performed with a real monitoring system with reference measure ments. The correct functionality of the measurement system was verified.
“…As the measurement of rotations has many advantages in comparison with that of deflections, several methods to estimate the bridge deflection curves based on the observation of rotations have arisen [16][17][18].…”
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