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Type:

Package

Title:

Estimating Remaining Useful Life with Linear Mixed Effects Models

Description:

Provides tools for estimating the Remaining Useful Life (RUL) of degrading systems using linear mixed-effects models and creating a health index. It supports both univariate and multivariate degradation signals. For multivariate inputs, the signals are merged into a univariate health index prior to modeling. Linear and exponential degradation trajectories are supported (the latter using a log transformation). Remaining Useful Life (RUL) distributions are estimated using Bayesian updating for new units, enabling on-site predictive maintenance. Based on the methodology of Liu and Huang (2016) <doi:10.1109/TASE.2014.2349733>.

Version:

1.0.0

License:

GPL-3

Encoding:

UTF-8

RoxygenNote:

7.2.1

Imports:

dplyr, nlme, quadprog, ggplot2

Maintainer:

Pedro Abraham Montoya Calzada <pedroabraham.montoya@gmail.com>

Depends:

R (≥ 4.5)

LazyData:

true

NeedsCompilation:

Packaged:

2025-08-19 07:44:02 UTC; Abraham

Author:

Pedro Abraham Montoya Calzada

[aut, cre, cph], Rogelio Salinas Gutiérrez

[aut, cph], Silvia Rodríguez-Narciso

[aut, cph], Netzahualcóyotl Castañeda-Leyva

[aut, cph]

Repository:

CRAN

Date/Publication:

2025-08-25 08:00:08 UTC

Remaining Useful Life (RUL) Ground Truth for FD001 Dataset

Description

Ground truth values of the Remaining Useful Life (RUL) for each engine unit in the FD001 subset of the C-MAPSS dataset. These values correspond to the last observed cycle in the test set and are used for evaluation purposes in prognostics models.

Usage

data("RUL_FD001")

Format

A data frame with 100 observations on the following variable:

RUL: Numeric vector indicating the true Remaining Useful Life (in cycles) for each unit in the test set.

Details

This dataset is part of the C-MAPSS (Commercial Modular Aero-Propulsion System Simulation) benchmark and is used as ground truth for performance evaluation of predictive maintenance models, particularly for models estimating Remaining Useful Life (RUL) under the FD001 operating condition scenario.

References

Saxena, A., Goebel, K., Simon, D., & Eklund, N. (2008). Damage propagation modeling for aircraft engine run-to-failure simulation. In 2008 International Conference on Prognostics and Health Management (pp. 1–9). IEEE. doi:10.1109/PHM.2008.4711414

Examples

data(RUL_FD001)

Constructing the Health Index on New Data Using Trained Weights

Description

Given a fitted "healthindex" object, this function constructs the univariate health index for new multivariate sensor data by applying the stored projection (weights and offsets).

Usage

compute_healthindex(model, data)

Arguments

model

An object of class "healthindex" returned by fit_healthindex.

data

A data frame with new sensor readings over time. Must include the columns t (time) and unit (unit identifier), plus the same set of degradation signals used at training. All degradation signals must follow an upward trend.

Details

This function applies the projection learned in the first stage of fit_healthindex to new data:

Value

A data frame (tibble) with the columns:

unit

Unit identifier.

t

Time index.

x

Constructed health index at each (unit, t).

Examples

library(degradr)
library(dplyr)
# Load example data
data(train_FD001)
data(test_FD001)
data <- train_FD001 %>%
  select(unit,t,T24,T50,P30,
         Nf,Ps30,phi, NRf,
         BPR,htBleed,
         W31, W32) %>%
  mutate(across(c(P30,phi,W31,W32), ~ . * -1))

test <- test_FD001 %>%
  select(unit,t,T24,T50,P30,
         Nf,Ps30,phi, NRf,
         BPR,htBleed,
         W31, W32) %>%
  mutate(across(c(P30,phi,W31,W32), ~ . * -1))

# Fit a health index model (exponential trajectory of degree 2)
model <- fit_healthindex(data = data, type = "exponential",
                         degree = 2, r = 0.8)

# Construct the health index on new data using stored weights/offsets
hi_new <- compute_healthindex(model = model, data = test)
head(hi_new)

Test data for filter degradation and RUL prediction

Description

Test data from a real-world degradation process involving the clogging of gas filters. The dataset includes right-censored lifetimes due to a preventive maintenance policy. Failure is defined when pressure differential exceeds 600 Pa.

Usage

data(filter_test)

Format

A data frame with 50 degradation trajectories. Variables include:

Time: Time
Differential_pressure: Differential pressure across the filter in Pascal (Pa).
Data_No: Unique identifier for each filter test unit. Integer from 1 to 50.
RUL: Remaining Useful Life in hours. Represents the time left until failure (threshold = 600 Pa).

Source

Adapted from:
Hagmeyer, S., Mauthe, F., & Zeiler, P. (2021). Creation of Publicly Available Data Sets for Prognostics and Diagnostics Addressing Data Scenarios Relevant to Industrial Applications. International Journal of Prognostics and Health Management, 12(2). doi:10.36001/ijphm.2021.v12i2.3087

References

See full description in the dataset repository on Kaggle by "Prognostics @ HSE".

Training Data for Filter Degradation and RUL Prediction

Description

Training data from a real-world degradation process involving the clogging of gas filters. The dataset includes right-censored lifetimes due to a preventive maintenance policy. Failure is defined when pressure differential exceeds 600 Pa.

Usage

data(filter_train)

Format

A data frame with 49 degradation trajectories. Variables include:

Time: Time
Differential_pressure: Differential pressure across the filter in Pascal (Pa).
Data_No: Unique identifier for each filter test unit. Integer from 1 to 50.

Source

References

See full description in the dataset repository on Kaggle by "Prognostics @ HSE".

Fitting a Health Index Model from Multivariate Signals

Description

Fits a health index–based degradation model by projecting multivariate sensor signals into a univariate health index and modeling its evolution using a linear mixed-effects model.

Usage

fit_healthindex(data,
  type = "exponential",
  method = "lm",
  degree = 2,
  phi = NULL,
  r = 0.5)

Arguments

data

A data frame containing sensor readings over time. Must include the columns t (time), unit (unit identifier), and multiple degradation signals. All degradation signals must have an upward trend.

type

Model type. Either "linear" or "exponential". The exponential model applies a logarithmic transformation to x - phi. Default is "exponential".

method

Estimation method. Either "nlme" to fit a nonlinear mixed-effects model using nlme::lme(), or "lm" to fit separate linear models per unit and estimate fixed and random effects from the set of coefficients. Default is "lm".

degree

Degree of the polynomial model. Default is 2. The fixed and random effects will include powers of time up to the specified degree.

phi

Initial degradation level for non-defective units. Used in the exponential model as a fixed offset to ensure that the logarithmic transformation is valid and interpretable. If NULL, it is automatically estimated as a value slightly below the minimum observed degradation level. Ignored when type = "linear".

r

parameter that controls the relative importance of the threshold variance and the weighted residual sum of squares in the index-fitted degradation model.

Details

This function implements a two-stage modeling strategy. In the first stage, a univariate health index is constructed as a weighted linear combination of the input signals, using correlation-based shrinkage. In the second stage, the resulting health index is modeled over time with a linear mixed-effects model (on the log scale for exponential models).

The exponential model uses a log transformation of x - phi, where phi ensures positivity and interpretability. The phi parameter can be supplied by the user or estimated automatically.

The resulting object stores both the projection (health index definition) and the fitted model used for RUL prediction.

Value

Returns an object of class "healthindex", which contains:

index

A list with components: weights w, offset phi, and raw projections.

model

A fitted mixed-effects model of the health index over time.

References

Liu, K. and Huang, S. (2016). Integration of Data Fusion Methodology and Degradation Modeling Process to Improve Prognostics. IEEE Transactions on Automation Science and Engineering, 13(1), 344–354.doi:10.1109/TASE.2014.2349733

Examples

library(degradr)
library(dplyr)
# Load example data
data(train_FD001)
data(test_FD001)
data <- train_FD001 %>%
  select(unit,t,T24,T50,P30,
         Nf,Ps30,phi, NRf,
         BPR,htBleed,
         W31, W32) %>%
  mutate(across(c(P30,phi,W31,W32), ~ . * -1))

test <- test_FD001 %>%
  select(unit,t,T24,T50,P30,
         Nf,Ps30,phi, NRf,
         BPR,htBleed,
         W31, W32) %>%
  mutate(across(c(P30,phi,W31,W32), ~ . * -1))

# Fit a health index model (exponential trajectory of degree 2)
model <- fit_healthindex(data = data, type = "exponential",
                         degree = 2, r = 0.8)
rul <- predict_rul(data = test, model = model)
head(rul)

Fitting the Linear Mixed Effects Model

Description

Fits a linear or exponential mixed-effects model of degree \(p\) for the degradation process.

Usage

fit_model(data,
  type = "exponential",
  method = "lm",
  degree = 2,
  phi = NULL)

Arguments

data

A data frame with three columns: t for time, x for the degradation signal, and unit as the unit identifier. At least two distinct units are required.

type

Model type. Either "linear" or "exponential". The exponential model applies a logarithmic transformation to x - phi. Default is "exponential".

method

degree

Degree of the polynomial model. Default is 2. The fixed and random effects will include powers of time up to the specified degree.

phi

Details

This function fits a linear or exponential polynomial mixed-effects model of degree p to degradation data collected over time from multiple units. The model captures both fixed effects (population-level degradation trends) and random effects (unit-specific deviations).

The exponential model applies a logarithmic transformation with an offset parameter phi. The offset phi can be provided or automatically estimated from the data.

At least two distinct units are required to estimate random effects. The degree parameter controls the polynomial order for the time terms in both fixed and random effects.

Value

Returns a list with the estimated model and prior distributions.

References

Examples

library(degradr)

# Load example data sets
data(filter_train)
data(filter_test)

# Show the original column names
colnames(filter_train)

# Rename the columns to match the expected format: t, x, unit
colnames(filter_train) <- c("t", "x", "unit")
colnames(filter_test)  <- c("t", "x", "unit", "RUL")

# Plot the training set
plot_degradr(data = filter_train, D = 600)

# Fit an exponential mixed-effects model of degree 1
model <- fit_model(data = filter_train, type = "exponential", degree = 1)

# Predict the remaining useful life (RUL) for the test units,
# assuming a fixed failure threshold D = 600
predict_rul(data = filter_test, model = model, D = 600)

Plot Degradation Trajectories for Multiple Units

Description

Generates a line plot of degradation signals over time for each unit, optionally overlaying a failure threshold line. This function is useful for visualizing degradation paths across multiple components or systems.

Usage

plot_degradr(data, D = NULL)

Arguments

data

A data frame with three columns: t for time, x for the degradation signal, and unit as the unit identifier.

D

Optional numeric value indicating the failure threshold.

Details

The function is designed to work with degradation datasets where each row represents an observation of a unit at a particular time. The plot shows how the degradation variable x evolves over time t for each unit. This is especially useful for visual inspection before model fitting or threshold analysis.

Value

Returns a ggplot object that can be further customized or directly printed.

Examples

library(degradr)

# Load example data sets
data(filter_train)
data(filter_test)

# Show the original column names
colnames(filter_train)

# Rename the columns to match the expected format: t, x, unit
colnames(filter_train) <- c("t", "x", "unit")
plot_degradr(data = filter_train, D = 600)

Predicting Remaining Useful Life (RUL) from Degradation Signals

Description

Estimates the Remaining Useful Life (RUL) for one or more partially observed degradation signals based on a previously fitted linear or exponential mixed-effects model.

Usage

predict_rul(data, model, D = NULL, upper = NULL)

Arguments

data

A data frame with columns t (time), x (degradation measurement), and unit (unit identifier). Multiple units can be passed simultaneously.

model

An object of class "degradation_model" produced by the fit_model function.

D

(Optional) Critical degradation threshold. If provided, it will be used to compute the RUL via a fixed-threshold model. If NULL (default), a random-threshold model will be used based on training data statistics.

upper

Optional upper bound for the search interval when solving for the quantiles of the RUL distribution. If NULL, the function will use the maximum observed time in the training data.

Details

This function applies Bayesian updating to compute the posterior distribution of the degradation model parameters for each unit, conditional on its observed signal. Then, it computes the Remaining Life Distribution (RLD) and returns the estimated Remaining Useful Life.

It supports both linear and exponential degradation models, matching the formulation used in fit_model. The posterior updating follows the methodology of Liu and Huang (2016).

Value

A data frame with one row per unit and the following columns:

unit: Unit identifier.
RUL: Estimated RUL.

References

Examples

library(degradr)

# Load example data sets
data(filter_train)
data(filter_test)

# Show the original column names
colnames(filter_train)

# Rename the columns to match the expected format: t, x, unit
colnames(filter_train) <- c("t", "x", "unit")
colnames(filter_test)  <- c("t", "x", "unit", "RUL")

# Plot the training set
plot_degradr(data = filter_train, D = 600)

# Fit an exponential mixed-effects model of degree 1
model <- fit_model(data = filter_train, type = "exponential", degree = 1)

# Predict the remaining useful life (RUL) for the test units,
# assuming a fixed failure threshold D = 600
predict_rul(data = filter_test, model = model, D = 600)

NASA Turbofan Engine Degradation Simulation Test Data (Subset FD001)

Description

Truncated time series data from turbofan engine degradation simulations, generated using the C-MAPSS (Commercial Modular Aero-Propulsion System Simulation) model. This test dataset contains operational sensor data up to a point before failure, intended for validating prognostic algorithms that estimate Remaining Useful Life (RUL).

Format

A data frame with multiple observations (rows) on the following 24 variables (columns):

unit: Engine unit number (identifier)
t: Time in cycles
T2: Total temperature at fan inlet (°R)
T24: Total temperature at LPC outlet (°R)
T30: Total temperature at HPC outlet (°R)
T50: Total temperature at LPT outlet (°R)
P2: Pressure at fan inlet (psia)
P15: Total pressure in bypass-duct (psia)
P30: Total pressure at HPC outlet (psia)
Nf: Physical fan speed (rpm)
Nc: Physical core speed (rpm)
epr: Engine pressure ratio (P50/P2)
Ps30: Static pressure at HPC outlet (psia)
phi: Ratio of fuel flow to Ps30 (pps/psi)
NRf: Corrected fan speed (rpm)
NRc: Corrected core speed (rpm)
BPR: Bypass Ratio
farB: Burner fuel-air ratio
htBleed: Bleed Enthalpy
Nf_dmd: Demanded fan speed (rpm)
PCNfR_dmd: Demanded corrected fan speed (rpm)
W31: HPT coolant bleed (lbm/s)
W32: LPT coolant bleed (lbm/s)

Details

Key characteristics of this test dataset:

Simulates progressive degradation in the High Pressure Compressor (HPC) module
Time series are truncated prior to failure (true RUL values not included)
Includes realistic measurement noise and unit-to-unit variability

References

Examples

data(test_FD001)

NASA Turbofan Engine Degradation Simulation Data (FD001)

Description

Run-to-failure simulation data for aircraft turbofan engines generated using C-MAPSS (Commercial Modular Aero-Propulsion System Simulation). This dataset represents engine degradation in the High Pressure Compressor (HPC) module under varying operational conditions.

Usage

data("train_FD001")

Format

A data frame with multiple observations (rows) on the following 24 variables (columns):

unit: Engine unit number (identifier)
t: Time in cycles
T2: Total temperature at fan inlet (°R)
T24: Total temperature at LPC outlet (°R)
T30: Total temperature at HPC outlet (°R)
T50: Total temperature at LPT outlet (°R)
P2: Pressure at fan inlet (psia)
P15: Total pressure in bypass-duct (psia)
P30: Total pressure at HPC outlet (psia)
Nf: Physical fan speed (rpm)
Nc: Physical core speed (rpm)
epr: Engine pressure ratio (P50/P2)
Ps30: Static pressure at HPC outlet (psia)
phi: Ratio of fuel flow to Ps30 (pps/psi)
NRf: Corrected fan speed (rpm)
NRc: Corrected core speed (rpm)
BPR: Bypass Ratio
farB: Burner fuel-air ratio
htBleed: Bleed Enthalpy
Nf_dmd: Demanded fan speed (rpm)
PCNfR_dmd: Demanded corrected fan speed (rpm)
W31: HPT coolant bleed (lbm/s)
W32: LPT coolant bleed (lbm/s)

Details

The data was generated for the Prognostics and Health Management (PHM) 2008 data challenge. Each engine unit starts with some initial wear and progresses to failure as efficiency and flow parameters degrade exponentially. The failure criterion is when the health index (calculated from stall margins and EGT) reaches zero. The dataset includes sensor measurements taken at cruise conditions.

References

Examples

data(train_FD001)

Remaining Useful Life (RUL) Ground Truth for FD001 Dataset

Description

Usage

Format

Details

References

Examples

Constructing the Health Index on New Data Using Trained Weights

Description

Usage

Arguments

Details

Value

See Also

Examples

Test data for filter degradation and RUL prediction

Description

Usage

Format

Source

References

Training Data for Filter Degradation and RUL Prediction

Description

Usage

Format

Source

References

Fitting a Health Index Model from Multivariate Signals

Description

Usage

Arguments

Details

Value

References

Examples

Fitting the Linear Mixed Effects Model

Description

Usage

Arguments

Details

Value

References

Examples

Plot Degradation Trajectories for Multiple Units

Description

Usage

Arguments

Details

Value

Examples

Predicting Remaining Useful Life (RUL) from Degradation Signals

Description

Usage

Arguments

Details

Value

References

Examples

NASA Turbofan Engine Degradation Simulation Test Data (Subset FD001)

Description

Format

Details

References

Examples

NASA Turbofan Engine Degradation Simulation Data (FD001)

Description

Usage

Format

Details

References

Examples