1. Center for Wireless Integrated MicroSensing & Systems
TRB sensor layout map
 Telegraph Road Bridge
 Stationary Bridge Sensor Network
Vehicle-induced vibration is one of the primary factors that accelerate bridge aging and
deterioration. Reducing the dynamic response of bridges to moving truck loads can be an
effective way of reducing long-term deterioration and extending bridge service lives.
This study introduces a wireless monitoring system architecture that integrates a mobile
wireless sensor network installed in a heavy truck to measure truck location and
vibrations with a stationary wireless sensor network installed on a bridge. Time-
synchronized truck-bridge response data collected can be used as the basis for modeling
vehicle-bridge interaction (VBI). The coupling of truck-based sensors and bridge
monitoring systems can be extended to potentially control the dynamics of trucks with
the aim of minimizing dynamic bridge responses. The proposed wireless VBI monitoring
and control system will be experimentally validated on the Telegraph Road Bridge (TRB)
using a calibrated tractor-trailer truck instrumented with a wireless sensor network.
Rui Hou, Yilan Zhang, Sean O’Connor, Jerome P. Lynch
Department of Civil and Environmental Engineering, University of Michigan, Ann Arbor
Vehicle-Bridge Interaction Test
Wireless Monitoring System
Monitoring and Control of Moving Truck Loads to Mitigate Vehicle-Induced Bridge Responses
Truck Loads Control
FurtherWork
The Telegraph Road Bridge (TRB)
is a three span highway bridge
located in Monroe, Michigan. The
main structure of the TRB is
composed of seven steel girders
supporting a reinforced concrete
adasdeck. The total length of the bridge is 224 ft. (68.28 m) including a main span of 140 ft.
(42.67 m) and two end spans of 48 ft. (14.63 m) each.
A network of Narada wireless
sensor nodes and an on-site
server managing the sensor
system are used to monitor the
bridge. With girders being the
primary load-carrying
members, 15 accelerometers
and 18 strain gages are
installed on them to measure
bridge responses during the
truck-bridge interaction. In
sad
 Mobile Truck Sensor Network
Axle
accelerometer
Chassis
accelerometer
GPS
system
Narada
node
Axle1
FrontAxleof
Tractor
Axle2
RearAxleof
Tractor
Axle3
TandemAxle
ofTrailer
Axle4
Axle1
FrontAxleof
Tractor
Axle2
RearAxleof
Tractor
Axle3
TandemAxle
ofTrailer
Axle4
Axle1
FrontAxleof
Tractor
Axle2
RearAxleof
Tractor
Axle3
TandemAxle
ofTrailer
Axle4
Instrumented test truck
: Acc. (chassis)
: Acc. (axles)
: Acc. (truck body)
: GPS antenna
The mobile truck sensor network is
installed in a four-axle tractor-trailer
truck. The distance between the first
axle and the last axle is 16.69 m. 20
accelerometers are installed in the
truck in total. There are two
accelerometers installed at each axle
and other two at the chassis at the
positions above each axle, at both
right and left sides. A Narada sensor
node encapsulating two vertical
accelerometers and two horizontal
accelerometers is installed at tractor
body near its center of gravity.
Besides, the truck is also
instrumented with a GPS module to
record its speed and location while
traversing the bridge.
LABORATORY for INTELLIGENT
SYSTEMS & TECHOLOGIES
Several vehicle-bridge interaction field tests were conducted on the TRB using the instrumented
test truck. The responses of the bridge and the truck were measured simultaneously by the
integrated wireless sensor network. The truck was driven over the bridge at three different speeds
(i.e., 53, 55, 60 mph) and these three kind of tests were conducted once, twice and six times,
respectively. The monitoring system was triggered before the truck entered the bridge and kept
recording the responses of the truck and the bridge using a sample rate of 200 Hz for 30 seconds
and then automatically stopped working until next VBI test. The collected truck-bridge vibration
data are time-synchronized by the recorded GPS time afterwards.
Introduction
addition, two laser sensors are installed at two end points of the bridge to detect the time
when the truck enters or departs the bridge and thus to calculate the average speed of the
truck while it is driven on the bridge.
Vehicle-Bridge Interaction Modeling
Bridge Dynamic Response:
 Girder vertical accelerations
 Girder dynamic bending strains
Truck Bouncing Behavior:
 Tractor body acceleration
 Trailer chassis accelerations
 Bridge Dynamics Parameters
 Truck Dynamics Parameters
 Truck Trajectory
VBI System
[𝐴, 𝐵 𝑘 , 𝐶]
Input Output
During the VBI process, the truck bounces vertically
while moving forward horizontally due to the bridge
surface roughness. In turn, this vehicle vibratory
behavior imposes extra dynamic loads to the bridge
apart from intrinsic static loads. Therefore, the VBI
system takes the vertical vibratory accelerations of
the tractor and trailer as inputs and takes bridge
responses (e.g., girder vertical accelerations or girder
Whole-vehicle Model & System Inputs
𝑢1
𝑢2 𝑢3
bending strains) which can be monitored by the wireless network as outputs. Consequently, the
VBI system can be described by a discrete-time multi-input multi-output state-space model.
𝑥 𝑘 + 1 = 𝐴𝑥 𝑘 + 𝐵 𝑘 𝑢 𝑘 + 𝑤(𝑘)
𝑦 𝑘 = 𝐶𝑥 𝑘 + 𝑣(𝑘)
 State-space VBI System Model
Notation (at time-step k):
 System input: 𝑢 𝑘 ∈ℜ3×1
 System matrix: 𝐴∈ℜ 𝑛×𝑛
 Output matrix: 𝐶∈ℜ𝑙×𝑛
 Measurement noise: 𝑣(𝑘)∈ℜ𝑙×1
 𝐵 𝑘 is time-varying due to the position-changing nature of the input
 System output: 𝑦 𝑘 ∈ℜ𝑙×1
 Input matrix: 𝐵∈ℜ 𝑛×3
 Process noise: 𝑤 𝑘 ∈ℜ 𝑛×1
 VBI System Identification
Objective: To estimate system matrix 𝐴, output matrix 𝐶 and time-varying input matrix 𝐵 𝑘
given system input and output data.
Identification Method:
Forced Vibration Free Vibration
Stage 2:
𝑥 𝑘 + 1 = 𝐴𝑥 𝑘 + 𝑩 𝒌 𝑢 𝑘
𝑦 𝑘 = 𝐶𝑥(𝑘)
Stage 1:
𝑥 𝑘 + 1 = 𝑨𝑥 𝑘
𝑦 𝑘 = 𝑪𝑥(𝑘)
Time History of
System Output:
Bridge Vibration
Time History of
System Input :
Truck Bouncing
Estimate time-invariant
system component
by stochastic subspace
identification method
No Input
Estimate 𝑩 𝒌 by least-squares
method to minimize the
difference between predicted
response and measured response
Given the identified VBI system model, it
is potentially an effective way of reducing
the system outputs (i.e., vehicle-induced
bridge vibration) by the control of the
system inputs (i.e., vehicle vertical
vibratory accelerations). An active actuator
is proposed to be installed on the truck to
apply a time-varying control force to the
truck so as to control the system inputs.
Since the axle weight of the last two axles
are larger than that of the axles under the
tractor, the actuator will be installed on the
trailer to control the last two inputs, 𝑢2and
𝑢3.dasddddddddddddddd
 Active Control Strategy
Truck axle static weight (in Lbs.)
Axle 1 Axle 2 Axle 3 Axle 4 Total
Weight 9460 17620 17820 17600 62500
Active Control Strategy
𝑢1
𝑢2 𝑢3
Control
Force
Actuator
 Optimal Control Algorithm
Results
Linear Quadratic Regulator (LQR) is performed to the identified VBI system to compute
optimal feedback gain that minimizing the system outputs.
LQR Type:
Discrete-time; time-varying, finite-horizon
Objective:
Minimize the cost function with system constraints (𝜆 - co-state, 𝑅 – weighting factor
matrix).
𝐽 =
1
2
𝑘=1
𝑛
𝑦 𝑇 𝑘 𝑦 𝑘 + 𝑢 𝑇 𝑘 𝑅𝑢 𝑘 +
𝑘=1
𝑛−1
𝜆 𝑇(𝑘 + 1) 𝑥 𝑘 + 1 − 𝐴𝑥 𝑘 − 𝐵 𝑘 𝑢(𝑘)
Closed-loop System:
𝑥 𝑘 + 1 = 𝐴𝑥 𝑘 + 𝐵 𝑘 [𝐾 𝑘 𝑥 𝑘 + 𝑣 𝑘 ]
𝑦 𝑘 = 𝐶𝑥(𝑘)
Notation (at time-step k):
𝐾 𝑘 is the derived feedback gain at time-step k.
𝐾 𝑘 𝑥 𝑘 is the auxiliary accelerations generated by the control force.
𝑣 𝑘 is the accelerations induced by the bridge surface roughness.
 System Identification Result  System Control Simulation
Predicted bridge response fit the measured
bridge response well
Vehicle-induced bridge vibration can be
reduced via truck loads control
 Establish physically meaningful (white-box) and time-invariant VBI system model
 Develop embedded system to implement the derived control law
 Conduct field experiments to validate the proposed control strategy