LIFETIME PREDICTION 

FOR DEGRADATION OF SOLAR MIRRORS 

USING STEP-STRESS ACCELERATED TESTING

ASTR 2011 Sept. 28-30, San Francisco, CA

NREL/PR-2C00-52658

NREL is a national laboratory of the U.S. Department of Energy, Office of Energy Efficiency and Renewable Energy, operated by the Alliance for Sustainable Energy, LLC.

Jinsuk Lee2

Ryan Elmore2

Cheryl Kennedy1

Matthew Gray1

Wesley Jones2

1 Resources & Building Systems Integration, National Renewable Energy Lab

2 Computational Science Center, National Renewable Energy Lab
 Concentrating Solar Power

 Reflectors of CSP

 Testing facility (Ultra-accelerated Weathering System)

 Optimal measurements

 Testing for lifetime prediction

 Step-stress accelerated degradation testing (SSADT)

 Multiple constant-stress accelerated degradation testing (MCSADT)

 Testing plans for UAWS

 Statistical procedure for lifetime prediction

 Degradation models for reflectors

 Statistical approaches for lifetime prediction

 Obtainable outputs

 Summary

Outline

ASTR 2011 Sept. 28-30, San Francisco, CA
 Introduce a cutting-edge life-testing technique, accelerated degradation testing (ADT) and 

its advanced testing technique, step-stress accelerated degradation testing (SSADT), for 

reliability testing of solar reflectors

 Design a durability testing plan for solar mirrors (3M’s new improved silvered acrylic “Solar 

Mirror Film (SMF) 1100”) through the ultra-accelerated weathering system (UAWS) 

 Develop statistical models for use of SSADT with the thermal-humidity-intensity stress 

condition through the cumulative damage model (CDM)

 Provide quantitative models for prediction of life-time including mean-time-to-failure 

(MTTF), warranty time and failure/degradation rates

 Estimate accelerated testing parameters, such as activation energy, acceleration factors, 

upper limit condition of stress via statistical inference procedure

 Define degradation paths of optical performance based on the SSADT model which is 

accelerated by high UV-radiant exposure, 

 Investigate appropriate physical degradation of reflectors

Objective of The Current Project

ASTR 2011 Sept. 28-30, San Francisco, CA
Concentrating Solar Power (CSP)

 CSP has currently four common Concentrating technologies:

 Parabolic trough  Solar power tower

 Linear Fresnel reflector  Dish-engine

Source: R. Paal (2008) [1]

Source: NREL

Source: NREL

Source: NREL

Source: NREL

Source: R. Paal (2008) [1] Source: R. Paal (2008) [1]

Source: R. Paal (2008) [1]
CSP Reflectors

ASTR 2011 Sept. 28-30, San Francisco, CA

 Reflectors (mirrors) and receiver tube coatings

are the major components of the solar field of

CSP systems.

 In evaluating the performance of these

materials, we can help to improve the overall

efficiency of CSP plants. Because the solar

field accounts for nearly half the total plants

construction cost, an increase in optical

efficiency can be a significant step toward

making CSP competitive with fossil fuels as a

utility-scale energy source.

 Three common reflective materials are 

commonly used for solar mirrors:

 Silvered Glass Mirrors (Thick and Thin Glass)

 Aluminized Mirrors

 Silvered Polymers

Anti-soiling Layer

PMMA superstrate

Adhesion Promoting Layer

Reflective Layer

Metal Back Layer

Pressure Sensitive Adhesive (PSA)

Substrate

Based on prior 3M/NREL collaborations

Source: Cheryl Kennedy, Advance CSP R&D, Solar 

Energy Technologies Program Peer Review, 2010

 Structure of 3M Polymer Reflector
 The UAWS is an outdoor weathering system, which

dramatically increases the UV radiant exposure per

unit time over what is attainable with current

moderately accelerated techniques. [1]

 The system allows a 63-year (approximate) equivalent

South Florida 45 UV-radiant exposure within a single

year of ultra-accelerated exposure. [1]

 The system provides high fidelity to natural solar UV

spectral power distributions while attenuating visible

and IR wavelengths to maintain acceptable specimen

exposure temperatures. [1]

 Polymer silvered reflectors are known to be

susceptible to degradation mechanisms associated

with exposure to UV radiation.

Ultra-Accelerated Weathering System (UAWS)

ASTR 2011 Sept. 28-30, San Francisco, CA
 Measure both hemispherical and specular reflectance using 

ultraviolet-visible-near infrared (UV-Vis-NIR) 

spectrophometers and specular reflectometers.

- Spectral hemispherical reflectance (ρ2π(λ))

- Specular reflectance (ρS(θ, λ))

 Optical performance is characterized in terms of specular 

reflectance, the degree to which a reflector is capable of 

transferring directed radiation to a target receiver surface. 

 Microroughness of a reflector surface, crazing of protective 

top coats, or both can result in scattering of light outside a 

specified angle, defined as the half angle (θ) subtended by 

the receiver as viewed from the reflector surface.

 The quantity ρ2π(λ) is measured in the wavelength range 

250 < λ < 2500 nm

 The specular reflectance is measured at a wavelength of 

660 nm

Optical Measurements

ASTR 2011 Sept. 28-30, San Francisco, CA

70mm diameter tube

e.g., if d=4667mm

θ=sin-1(35mm/4667mm)

then acceptance angle (2θ) =15mrad

d
ADT & SSADT

stress

time

stress

time

 Step-Stress Accelerated Degradation Test (SSADT)

 Step-stress testing is one of the most basic time-varying

stress tests. Ina step-stress test, multiple samples in one or

more sets are exposed to several stress conditions over time.

 Step-stress testing is an advanced reliability testing

technique for high reliability products.

o Economical: suitable when we are constrained by test

facilities, conditions, or samples

o Flexible: useful for developing products where there is not

enough knowledge for test conditions

 The accelerated life testing (ALT) technique may offer little

help for highly reliable products which are not likely to fail

duringa rather short period time.

 ADT relies on the degradation data instead of failure data

when it is more difficult to obtain sufficient failure data for ALT

but when degradation can be used to make acceptable

prediction of failure.

 Single constant-stress testing (e.g., Damp-Heat Test) can be

used for qualification testing witha specific durability criteria

 MCSADT can be used for life-time prediction of products.

 Multiple Constant-Stress Accelerated Degradation Test (MCSADT)
What is SSADT ?

 Degradation vs. Time plot degradation

time

.7

.5

.3

τ1 τ2 τ3

w1 w1 + (τ2 - τ1)

L(t | s0 =45 ̊C)

L(t | s0 =65 ̊C)

L(t | s0 =85 ̊C)

Cumulative Exposure Model
What is SSADT ?

 Degradation vs. Time plot degradation

time

.7

.5

.3

τ1 τ2 τ3

w1 w1 + (τ2 - τ1)

L(t | s0 =45 ̊C)

L(t | s0 =65 ̊C)

τ L(t | s0 =85 ̊C) 2 – τ1

Cumulative Exposure Model
What is SSADT ?

 Degradation vs. Time plot degradation

time

.7

.5

.3

τ1 τ2 τ3

w1 w1 + (τ2 - τ1)

w2 w2 + (τ3 – τ2)

L(t | s0 =45 ̊C)

L(t | s0 =65 ̊C)

L(t | s0 =85 ̊C)

Cumulative Exposure Model
What is SSADT ?

 Degradation vs. Time plot degradation

time

.7

.5

.3

τ1 τ2 τ3

w1 w1 + (τ2 - τ1)

w2 w2 + (τ3 – τ2)

L(t | s0 =45 ̊C)

L(t | s0 =65 ̊C)

L(t | s0 =85 ̊C)

Cumulative Exposure Model
What is SSADT ?

 Degradation vs. Time plot degradation

time

.7

.5

.3

τ1 τ2 τ3

w1 w1 + (τ2 - τ1)

w2 w2 + (τ3 – τ2)

L(t | s0 =45 ̊C)

L(t | s0 =65 ̊C)

L(t | s0 =85 ̊C)

Cumulative Exposure Model
 Adopt two separate SSADT plans, each of which is 

designed with two UV-radiant exposure

 Reflector samples are initially tested at 50X 

intensity until reaching a pre-determined switch time

 The stress is increased to 100X and the test 

continues as before

 During the testing, the specular reflectance of each 

sample is measured at pre-specified inspection 

times

Testing Plan

ASTR 2011 Sept. 28-30, San Francisco, CA

T (°C)

30°C

60°C

IUV

100X

Time (hrs)

50X

τ1 τ2

SSADT 1

SSADT 2

T (°C)

30°C

60°C

IUV

100X

τ Time (hrs) 2

CSADT 2

CSADT 1

 MCSADT

 SSADT

 Also consider a MCSADT plan, where two constant 

stress ADTs are deigned at two exposure 

temperatures of 30°C and 60°C, respectively

 Each test is subjected to 100X intensity throughout 

the pre-determined testing time
Degradation Model for Polymer Reflectors

ASTR 2011 Sept. 28-30, San Francisco, CA

 Stage 1: Define a physical relationship of stress for degradation rate

 UV radiance

 Temperature

 Humidity

 Stage 2: Identify the degradation pattern 

 Linear

 Exponential

 Power

 Logarithmic

 others (Tseng and Wen, 2000)

(Vehicle Battery)

 Stage 3: Build a proper degradation model

(Jorgensen et al., 1999 & Jorgensen 2003)

Choose “Power” with a = 1
 Inference of SSADT through Least Square Estimation (LSE)

 Construct the expected degradation for SSADT at each temperature

 Minimize the sum of square error

 Estimate the product lifetime, Activation Energy, degradation rate

 Detect the violation for the constant assumption with

by minimizing

 Determine the upper limit condition

Statistical Approach for Lifetime Prediction 

(Using SSADT)

ASTR 2011 Sept. 28-30, San Francisco, CA
 Inference of SSADT through Maximum Likelihood Estimation (MLE)

 Construct the likelihood function using the transformed data based on failure 

distributions

 (Alternative option) Transform to a generalized linear model form with the Bernoulli 

trial and solve the problem through the iterative weighted least square (IWLS) method

 Estimate the product lifetime (including warranty time and mean-time-to failure 

(MTTF)), Activation Energy, failure rate, etc.

Statistical Approach for Lifetime Prediction 

(Using SSADT)

ASTR 2011 Sept. 28-30, San Francisco, CA
 Product lifetime parameters at various use-conditions

- Mean time to failure

- Reliability (Warranty) time

- Failure rate & Degradation rate

 Degradation rate at various use-conditions

 Activation Energy (Ea)

 Upper limit level of stress 

(tolerable stress level)

What Can be Estimated from SSADT?

ASTR 2011 Sept. 28-30, San Francisco, CA

FL**

AZ*

80% 

Warranty

50% 

Warranty

 Example for Warranty Time

85°C/85%RH

110°C/85%RH

65°C/65%RH

55°C/65%RH

45°C/40%RH

α5=0.931*

α4=0.817+

α3=0.794*

α2=0.781*

α1=0.788*

 Example for Upper Limit Level of Stresses

*AZ (23.8°C & 34.5%RH)

**FL (24.2°C & 75.3%RH)
 Discuss lifetime prediction for metalized polymer reflectors

 Study the physical degradation models in optical performance, including 

UV-radiant exposure and thermal and moisture effects as relevant 

environmental stresses

 Develop accelerated testing plans for using the Ultra-Accelerated 

Weathering System (UAWS): considering step-stress accelerated 

degradation testing (SSADT) and multiple constant-stress accelerated 

degradation testing (MCSADT) techniques

 Develop statistical procedures for SSADT in order to predict lifetime of 

polymer reflectors

 Discuss several statistical approaches to enhance the lifetime prediction 

of reflectors

Summary

ASTR 2011 Sept. 28-30, San Francisco, CA
1. Edited by T. M. Letcher, Future Energy – Improved, Sustainable and Clean Options for Our Planet, Elsevier, Oxford, UK, 

2008

2. H. K. Hardcastle and G. J. Jorgensen, “Ultra-accelerated weathering system I: Design and functional considerations,”

Natural and Artificial Ageing of Polymers – 4th European Weathering Symposium; Reichert, T., Ed. Publication No. 11,

Gesellschaft für Umweltsimulation: Germany, 2009.

3. C. Kennedy, “Advanced Reflector and Absorber Materials (Thermal System Group: CSP Capabilities),” NREL/FS-550-

48662, 2010.

4. ASTM Standard E903-82. Standard Test Method for Solar Absorptance, Reflectance, and Transmittance of Materials

Using Integrating Spheres. In: Annual Book of ASTM Standards 1993, Vol. 12.02, pp. 512-520, American Society for

Testing and Materials, Philadelphia, PA, 2003.

5. W. Nelson, “Accelerated life testing – Step-stress models and data analysis,” IEEE Transactions on Reliability., Vol. 29,

pp. 103-108, 1980.

6. G. Jorgensen, C. Bingham, J. Netter, R. Goggin, and A. Lewandowski, "Chapter 11: A unique facility for ultra-accelerated

natural sunlight exposure testing of materials." From Service Life Prediction of Organic Coatings: A systems approach,

Bauer, D.R. and Martin, J.W. (Eds.), International Symposium on Service Life Prediction, 1997, Breckenridge, CO, ACS

Symposium Series 722, American Chemical Society, Washington, DC, 1999, pp. 170-185.

7. S. Tseng, Z. Wen, “Step-stress accelerated degradation analysis for highly reliable products,” Journal of Quality

Technology, 32, 2000, pp. 209-216.

8. J. Lee and R. Pan, “Analyzing step-stress accelerated life testing data using generalized linear models,” IIE Trans., 42,

2010, pp. 589-598.

Key Reference

ASTR 2011 Sept. 28-30, San Francisco, CA
Acknowledgements

ASTR 2011 Sept. 28-30, San Francisco, CA

 This work was supported by the U.S. Department of Energy under 

Contract No. DE-AC36-08-GO28308 with the National Renewable Energy 

Laboratory.
Thank You !!!

ASTR 2011 Sept. 28-30, San Francisco, CA