The temperature changed when I was measuring strain, whose data should I use?
In Fiber Bragg Grating (FBG) sensing technology, the phenomenon you’ve encountered is known in physics and sensor engineering as “Cross-sensitivity”.
Simply put, it means FBGs are simultaneously sensitive to both “strain” and “temperature”. When you are measuring structural strain, if the ambient temperature changes, the signal reflected by the sensor will be a superposition of both effects, making it impossible to directly determine the true strain value from a single data source.
Below, we will delve into the essence of “cross-sensitivity” and the solutions for “who should you listen to?” from both the physical principles and engineering application perspectives.
I. Physical Principles: Why Does Cross-sensitivity Occur?
The center reflection wavelength (Bragg wavelength) of an FBG, \lambda_B , is determined by the fundamental physical formula:
\lambda_B = 2 n_{\text{eff}} \Lambda
Where:
- n_{\text{eff}} is the effective refractive index of the fiber core.
- \Lambda is the grating period.
When the sensor is simultaneously affected by physical stretching (strain) and temperature changes, these two physical quantities alter n_{\text{eff}} and \Lambda through different physical mechanisms:
- Strain Effect ( \Delta \varepsilon ): Directly stretches or compresses the fiber, changing its grating period \Lambda ; simultaneously alters the refractive index n_{\text{eff}} through the Photoelastic effect.
- Temperature Effect ( \Delta T ): Changes the grating period \Lambda through thermal expansion; simultaneously alters the refractive index n_{\text{eff}} through the Thermo-optic effect.
Therefore, when strain and temperature change simultaneously, the total drift of the reflection wavelength \Delta \lambda_B is a linear superposition of both:
\Delta \lambda_B = \alpha_{\varepsilon} \Delta \varepsilon + \alpha_T \Delta T
Where:
- \alpha_{\varepsilon} is the strain sensitivity coefficient. For the standard 1550\text{ nm} wavelength band, the strain coefficient for a bare FBG is \alpha_{\varepsilon} \approx 1.2\text{ pm}/\mu\varepsilon .
- \alpha_T is the temperature sensitivity coefficient. In the bare grating state, \alpha_T \approx 10\text{ pm}/^\circ\text{C} (this coefficient can change significantly depending on the thermal expansion coefficient of the packaging material if it is encapsulated).
Who Should You Listen To?
Since the interrogator ultimately measures only a combined wavelength change \Delta \lambda_B , you cannot determine from this single value whether it is caused by 100\ \mu\varepsilon of mechanical strain or 12\ ^\circ\text{C} of temperature fluctuation.
II. Solutions: How to Isolate Temperature Interference?
To accurately measure the true strain in an environment with constantly changing temperatures, Temperature Compensation must be introduced. In engineering practice, the following methods are mainly employed:
1. Dual Grating Temperature Compensation Method (Co-located/Adjacent Temperature Compensation) — The Most Classic and Commonly Used
Install a stress-free reference FBG temperature sensor adjacent to the strain measurement point.
- Strain Sensor (FBG 1): Subjected to both structural stress and temperature changes. Its wavelength drift is:\Delta \lambda_{B1} = \alpha_{\varepsilon1} \Delta \varepsilon + \alpha_{T1} \Delta T
- Temperature Sensor (FBG 2): Due to its special stress-free packaging structure, it does not bear any external mechanical structural strain (i.e., \Delta \varepsilon = 0 ). Its wavelength drift is purely caused by local temperature changes:\Delta \lambda_{B2} = \alpha_{T2} \Delta T
Using the drift from FBG 2, we can calculate the real-time temperature change \Delta T . Substituting this into the equation for FBG 1 allows for complete removal of temperature-induced drift, calculating the pure mechanical strain:
\Delta \varepsilon = \frac{\Delta \lambda_{B1} - \frac{\alpha_{T1}}{\alpha_{T2}} \Delta \lambda_{B2}}{\alpha_{\varepsilon1}}
If both gratings have consistent temperature sensitivity during factory calibration ( \alpha_{T1} = \alpha_{T2} ), the formula can be further simplified to:
\Delta \varepsilon = \frac{\Delta \lambda_{B1} - \Delta \lambda_{B2}}{\alpha_{\varepsilon1}}
2. Dual Wavelength/Birefringence Matrix Algorithm
Utilize two sensing elements with significantly different material physical properties. Construct a system of two linear equations at the same measurement point:
$$ \begin{bmatrix} \Delta \lambda_1 \ \Delta \lambda_2 \end{bmatrix} = \begin{bmatrix} \alpha_{\varepsilon1}
\alpha_{T1} \ \alpha_{\varepsilon2}
\alpha_{T2} \end{bmatrix} \begin{bmatrix} \Delta \varepsilon \ \Delta T \end{bmatrix} $$
As long as the sensitivity matrix is full rank, the true strain and temperature can be obtained simultaneously by solving the inverse matrix. However, this method involves a complex calibration process and has slightly lower engineering stability compared to the dual grating method.
III. OFSCN® (Dacheng Yongsheng) Professional Engineering Advice and Product Portfolio
In actual engineering tests, although temperature-compensating gratings can be integrated within a single strain sensor, due to packaging thermal inertia and local micro-stress transfer, we strongly recommend using external, independent, stress-free FBG temperature sensors for temperature compensation to achieve the highest accuracy.
Here are the targeted products and recommended combination solutions provided by Beijing Dacheng Yongsheng Technology Co., Ltd. (OFSCN®):
-
Structural Strain Measurement Sensor:
OFSCN® Polymer-encapsulated Fiber Bragg Grating Strain Sensor (1.5mm/2.3mm diameter)
This product uses polymer material to encapsulate the FBG and is equipped with a seamless stainless steel protective sleeve, ensuring extremely high strain transfer efficiency and waterproofing. The sensors are rigorously calibrated for strain at the factory. It is recommended for use with external temperature compensation sensors. -
Independent Stress-Free Temperature Compensation Sensor:
OFSCN® 500°C Fiber Bragg Grating Temperature Sensor
This product uses precision stress-free stainless steel tube encapsulation. The internal grating can slide freely and does not respond to any substrate deformation, specifically designed to provide high-precision local temperature reference values, perfectly addressing the \Delta T drift term in the aforementioned formulas.
For more packaging forms and system configurations of FBG strain measurement technology, you can refer to the relevant technical documentation via the OFSCN® FBG Strain Sensor Products Aggregation Link.