# Performance-Driven Measurement System Design for Structural Identification

## Summary (3 min read)

### INTRODUCTION

- Identifying and understanding the behaviour of civil structures based on measurement data is increasingly used for avoiding replacement and strengthening interventions (Catbas et al. 2012).
- Indeed, in many practical situations, the cost of making sense of data often exceeds by many times the initial cost of sensors.
- Furthermore, in the case of structural identification, measurement uncertainties are often not the dominant source of uncertainty (Goulet et al. 2010).
- This paper proposes a computer-aided measurement-system design methodology that includes systematic bias and epistemic uncertainties.

### PREDICTING THE PERFORMANCE OF MEASUREMENT SYSTEMS AT FALSIFYING MODELS

- Starting with the principle that observations can best support the falsification of hypotheses, the error-domain model-falsification approach (Goulet et al.
- Model instances are falsified if at any location i, the difference between predicted (gi(θ)) and measured (yi) values lies outside the interval defined by threshold bounds (Ti,Low, Ti,High) that are based on modeling and measuring uncertainties.
- The projection of threshold bounds including a probability φ′, determined for each combined uncertainty pdf, defines a square region that includes a probability content φ.
- These dependencies are described by correlation coefficients.
- This cdf describes the certainty of obtaining any number of candidate models if measurements are taken on the structure.

### MEASUREMENT-SYSTEM DESIGN

- The expected identifiability described in the previous section is used as a performance metric to optimize the efficiency of measurement systems.
- Therefore, the methodology also uses measurement-system cost as a second objective for optimizing measurement systems.
- Equation 2 presents the number of possible sensor configurations.
- In order to obtain optimized solutions efficiently, advanced search algorithms are necessary.

### Methodology

- The methodology used to design efficient measurement systems is based on a Greedy algorithm.
- At each iteration, it identifies the measurement that can be removed from an initial configuration containing N measurements while minimizing the expected number of candidate models.
- The results from measurement-system optimization are returned in a two-objective graph as presented in Figure 6 and in a table containing the details of each measurement-system configuration.
- Beyond this point, additional measurements may decrease the efficiency of the identification by increasing the number of candidate models (i.e. reducing the number of falsified models).
- Threshold corrections ensure that the reliability of the identification meets the target φ when multiple measurements are used simultaneously to falsify model instances.

### Complexity

- For static monitoring, if one load case is possible, the Greedy algorithm performs the measurement-system optimization in less than n2m/2 iterations, where nm is the maximal number of measurements.
- Figure 8 compares the number of iterations required with the number of sensor combinations possible for one load-case.
- It shows that Greedy algorithm complexity (O(n2)) leads to a number of sensor combinations to test that is significantly smaller than the number of possible combinations (O(2n)).

### CASE-STUDY

- The measurement-system design methodology presented in the previous section is used to optimize the monitoring system for investigating the behavior a full-scale structure using static load-tests.
- The Langensand Bridge is located in Lucerne, Switzerland.
- The primary parameters to identify are the concrete Young’s modulus for the slab poured during construction phase one and two, the asphalt Young’s modulus for phase one and two and the stiffness of the horizontal restriction that could take place at the longitudinally free bearing devices.
- The initial measurement system to be optimized is composed of ten displacement, four rotation and five strain sensors.
- Each test-truck weighs 35 tons and each test load-case takes two hours.

### Modeling and measurement uncertainties

- Several random and epistemic uncertainty sources affect the interpretation of data.
- These numbers are based on uncertainties defined by Goulet and Smith (2012) for a first study performed on the structure during its construction phase.
- This distribution is made of several orders of uniform distribution, each representing the uncertainty associated with the bound position.
- The correlation between predictions originating from secondary-parameter uncertainties is implicitly provided when uncertainties are propagated through the finite-element template model.
- Therefore, specific threshold bounds are computed for each sensor configuration.

### Measurement-system design results

- Measurement-system optimization is performed according to two criteria: loadtest costs and the expected number of candidate models.
- This quantitatively shows a principle, intuitively known by engineers, that too much measurement data may hinder interpretation.
- The sensor and load-case configurations associated with each dot in Figure 13 are reported in Table 3.
- The best measurement system found uses 4 sensors with 3 load-cases and would result in almost 80% of model instances to be falsified.
- This measurementsystem configuration is halfway between the cheapest and most expensive measurement systems.

### DISCUSSION

- Results presented here indicate that over-instrumenting a structure is possible.
- The methodology presented in this paper can be used with optimizations methodologies other than the Greedy algorithm.
- As it was already noted by (Goulet and Smith 2011c) the global trend of over instrumentation is independent of the optimization technique.
- Furthermore, for this case, a sensitivity analysis has shown that the effect of single sensor removal is dominant over the effect of the interaction caused by multiple sensor removal.
- Therefore, stochastic search algorithms are not expected to provide better optimization results.

### CONCLUSIONS

- Computer-aided measurement-system design supports cost minimization while maximizing expected efficiency identifying the behaviour of structures.
- The criteria used to falsify models (threshold bounds) are dependent upon the number of measurements, also known as Specific conclusions are.
- If too many measurements are used, data-interpretation can be hindered by over-instrumentation.
- The measurement-system design methodology can be used to determine good tradeoffs with respect to interpretation goals and available resources.
- Further work is under way to establish the usefulness of greedy sensor removal with respect to stochastic search methods for a range of cases.

Did you find this useful? Give us your feedback

##### Citations

117 citations

109 citations

### Cites background from "Performance-Driven Measurement Syst..."

...Keywords: System identification, leak detection, sensor placement, data interpretation, water distribution, uncertainty, error-domain model falsification...

[...]

61 citations

### Cites methods from "Performance-Driven Measurement Syst..."

...Model falsification has also been applied to sensor configuration [19, 33, 38]....

[...]

44 citations

### Cites background or methods from "Performance-Driven Measurement Syst..."

...166 As shown by Goulet and Smith [44], more measurements does not mean higher performance of structural 167 identification....

[...]

...Although several authors in various fields have pointed out the importance of providing36 an adequate description of modeling uncertainties associated with the model class [4, 19–22], proposals for37 robust alternatives to existing approaches are lacking.38 Goulet and Smith [3] proposed an approach that is robust when knowledge of the joint PDF of modeling39 and measurement errors is incomplete....

[...]

...Model falsification task: error-domain model falsification180 Proposed by Goulet and Smith [3], the error-domain model falsification approach aims to obtain possible181 values for θ = [θ1, . . . , θnθ ] ᵀ, describing a vector of nθ parameter values of a physics-based model using182 information provided by measurements....

[...]

...Although Goulet47 and Smith [3] have observed that EDMF can identify when initial assumptions related to the model class48 are erroneous by falsifying all model instances, taking advantage of this characteristic for exploring possible49 model classes of complex structures has not been studied.50 Choi and Beven [24] have also observed that model falsification could serve to point out model deficiencies51 in the search for a better model class....

[...]

...This work was funded by the Swiss National Science Foundation under Contract no.668 200020-155972.669 References670 [1] S. Atamturktur, Z. Liu, H. Cogan, S.and Juang, Calibration of imprecise and inaccurate numerical models considering671 fidelity and robustness: a multi-objective optimization-based approach, Structural and Multidisciplinary Optimization672 (2014) 1–13.673 [2] J. Beck, Bayesian system identification based on probability logic, Structural Control and Health Monitoring 17 (7) (2010)674 825–847.675 [3] J.-A. Goulet, I. Smith, Structural identification with systematic errors and unknown uncertainty dependencies, Computers676 & Structures 128 (2013) 251–258.677 [4] F. Çatbaş, T. Kijewski-Correa, A. Aktan, Structural identification of constructed systems, Reston (VI): American Society678 of Civil Engineers .679 [5] J. Beck, L. Katafygiotis, Updating models and their uncertainties....

[...]

43 citations

##### References

41,772 citations

37,111 citations

### "Performance-Driven Measurement Syst..." refers methods in this paper

...Several stochastic global search algorithms are available in the literature (Deb et al. 2002; Raphael and Smith 2003; Kirkpatrick et al. 1983; Kennedy and Eberhart 1995; Cormen 2001) with several applications in the field of civil engineering (Harp et al....

[...]

...Several stochastic global search algorithms are available in the literature (Deb et al. 2002; Raphael and Smith 2003; Kirkpatrick et al. 1983; Kennedy and Eberhart 1995; Cormen 2001) with several applications in the field of civil engineering (Harp et al. 2009; Dimou and Koumousis 2009; Domer et…...

[...]

35,104 citations

21,651 citations

##### Related Papers (5)

##### Frequently Asked Questions (2)

###### Q2. What are the future works mentioned in the paper "Performance-driven measurement-system design for structural identification" ?

Further work is under way to establish the usefulness of greedy sensor removal with respect to stochastic search methods for a range of cases.