Quantitative Shape Measurement of an Inflatable Rubber Dam Using an Array of Inertial Measurement Units

Shape measurement plays an important role in the condition monitoring and operation control of inflatable rubber dams. This paper presents a method to measure the cross-sectional shape of a rubber dam using an array of inertial measurement units (IMUs) placed on the circumference of the dam. Accelerometer and gyroscope measurements are combined using an adaptive complementary filter to determine the tangent angles of the dam circumference. The adaptive complementary filter adjusts the weights of the accelerometer and gyroscope measurements dynamically in order to reduce the uncertainty in orientation estimation due to external acceleration under dynamic conditions. A natural cubic spline that interpolates the measured tangent angles at discrete locations is used to represent the tangent angles along the dam circumference as a continuous function of the arc length. Finally, the cross-sectional shape is reconstructed by integrating the continuous tangent angle function along the circumference of the dam. Experimental assessment of the measurement system was performed on a purpose-built test rig using a digital camera as a reference measuring device. Results under a typical static condition show that the measured and reference shapes agree well with each other, with a similarity index of 3.74%, mismatch distance of the last IMU node being 12.3 mm and relative error of height measurement being -2.44%. Under dynamic conditions, the measurement results deteriorate due to external acceleration, but considerable improvement is achieved in comparison with an accelerometer-only approach. In addition, elimination of faulty nodes from shape reconstruction has negligible influence on the results, suggesting that the measurement system enjoys a high degree of fault tolerance.