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Explainable Predictive Maintenance: A Survey of Current Methods, Challenges and Opportunities

Logan Cummins, Alex Sommers, Somayeh Bakhtiari Ramezani, Sudip Mittal, Joseph Jabour, Maria Seale, Shahram Rahimi

arXiv:2401.07871v1cs.AIcs.HCcs.LG

TL;DR

Predictive maintenance increasingly informs consequential decisions, yet explanation evaluation and the needs of different users remain under-addressed. This review uses PRISMA to organize XAI and interpretable ML methods for PdM and synthesizes their applications and challenges. It identifies uneven explanation-metric use and offers candidate metrics and a human-involved evaluation approach.

  • Problem

    Explanation evaluation has received less attention than model-performance evaluation, and explainable systems still lack sufficient attention to the differing needs of their human users.

    Source: B. EVALUATION OF THE EXPLANATIONS · p. 20, C. ADDITION OF HUMAN INVOLVEMENT · p. 20

  • Method

    The review applies PRISMA to organize XAI and iML literature on PdM, categorizing the methods and discussing challenges and future research directions.

    Source: §I · p. 2, §VIII · p. 21

  • Results

    The 102-article review found anomaly detection to be the main task using XAI and iML, with prognosis leaning toward XAI and diagnosis toward iML.

    Source: C. INCLUSION · p. 4, §IV · p. 5

  • Takeaways & Limitations

    The review identifies limited use of explanation metrics in PdM, lists candidate metrics, and outlines gathering target-audience feedback to guide human-specified explanations.

    Source: §VIII · p. 21

    The survey covers only a small portion of potential XAI and iML literature and omits some popular methods and applicable algorithms.

    Source: D. STUDY LIMITATIONS · p. 21

Abstract

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Predictive maintenance is a well studied collection of techniques that aims to prolong the life of a mechanical system by using artificial intelligence and machine learning to predict the optimal time to perform maintenance. The methods allow maintainers of systems and hardware to reduce financial and time costs of upkeep. As these methods are adopted for more serious and potentially life-threatening applications, the human operators need trust the predictive system. This attracts the field of Explainable AI (XAI) to introduce explainability and interpretability into the predictive system. XAI brings methods to the field of predictive maintenance that can amplify trust in the users while maintaining well-performing systems. This survey on explainable predictive maintenance (XPM) discusses and presents the current methods of XAI as applied to predictive maintenance while following the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) 2020 guidelines. We categorize the different XPM methods into groups that follow the XAI literature. Additionally, we include current challenges and a discussion on future research directions in XPM.

I. INTRODUCTION

The paper frames predictive maintenance as a human-centered decision problem and surveys XAI and interpretable ML as ways to address it. It distinguishes explanation of a trained model’s outputs from interpretability built into the model itself.

I. INTRODUCTION

  • PdM research has emphasized models and system optimization, while the people affected by those systems have received less attention.The paper connects this shift toward human-centered processes with Industry 5.0.Source: §I · p. 1
  • The paper organizes XAI and iML work applied to PdM using PRISMA and categorizes methods, challenges, and future research directions.It presents this organization as its main contribution.Source: §I · p. 2

A. EXPLAINABILITY AND INTERPRETABILITY IN ARTIFICIAL INTELLIGENCE

  • Researchers disagree on whether explainability and interpretability are synonymous, distinct, or related as a subset and superset.The paper treats them as related but distinct, with some overlap.Source: A. EXPLAINABILITY AND INTERPRETABILITY… · p. 2

1) Explainable Artificial Intelligence

  • XAI primarily uses post-hoc methods to explain an already-trained model’s otherwise opaque workings and outputs.The aim is to support user comprehension of the model’s behavior.Source: 1) Explainable Artificial Intelligence · p. 2
  • XAI methods may be model-agnostic, such as SHAP and LIME, or model-specific, such as CAM for CNNs.The former can apply across architectures; the latter use features of a particular architecture.Source: 1) Explainable Artificial Intelligence · p. 2
  • XAI explanations can be local to one data point or global representations of model behavior across data points.These categories describe the scope of an explanation.Source: 1) Explainable Artificial Intelligence · p. 2

2) Interpretable Machine Learning

The paper distinguishes intrinsically interpretable ML from post-hoc explanation and situates PdM tasks in a PRISMA-based systematic search. Its search and screening process narrows candidate literature to studies focused on XAI or iML in PdM case studies that provide explanations or interpretations.

2) Interpretable Machine Learning

  • Interpretable ML uses architectural or physical constraints to make models intrinsically understandable, focusing on the model rather than its output.Architectural constraints simplify models, while physical constraints express computations through real-world features.Source: 2) Interpretable Machine Learning · p. 3

B. PREDICTIVE MAINTENANCE

  • PdM uses AI and prior failure information to predict future faults or downtime through anomaly detection, fault diagnosis, and prognosis.Anomaly detection identifies whether a fault occurred, diagnosis identifies its cause, and prognosis predicts remaining useful life or time until failure.Source: B. PREDICTIVE MAINTENANCE · p. 3

III. SYSTEMATIC SEARCH

  • The review used the PRISMA 2020 statement to structure its systematic literature-review methodology.The paper directs readers to Figure 3 for the process.Source: §III · p. 3

A. IDENTIFICATION

  • Searches of IEEE Xplore, ACM Digital Library, ScienceDirect, and Scopus used title, keyword, and abstract terms for XAI or iML and PdM.The databases were accessed on June 21, 2023; the initial pool contained 6932 articles, later reduced to 296 for initial screening.Source: A. IDENTIFICATION · pp. 3–4

B. EXCLUSION CRITERIA AND SCREENING

  • Initial screening excluded papers that did not focus on XAI or iML, were not PdM case studies, or provided no explanation or interpretation.The screening also removed articles that named an explanatory method without presenting its output; 116 articles were then sought for retrieval.Source: B. EXCLUSION CRITERIA AND SCREENING · p. 4
  • Final eligibility review read all available resources and excluded 11 of the 113 remaining articles for stated eligibility reasons.The listed reasons include papers that mentioned methods without using them, lacked interpretations, or did not focus on PdM experiments.Source: B. EXCLUSION CRITERIA AND SCREENING · p. 4

C. INCLUSION

The review retained 102 articles and found XAI slightly more common than iML in PdM. Its results are organized by maintenance task and its explainable-method discussion groups methods into model-agnostic, model-specific, and combination approaches.

C. INCLUSION

IV. SEARCH RESULTS

  • XAI is slightly more popular than iML in the reviewed PdM literature, with complex architectures and their black-box nature offered as a possible reason.Source: §IV · p. 5, Figure 6 · p. 5
  • Anomaly detection is the largest task group, while fault diagnosis and prognosis have similar article counts; prognosis leans toward XAI and diagnosis toward iML.Source: §IV · p. 5

V. EXPLAINABLE AI IN PREDICTIVE MAINTENANCE

  • The XAI methods are divided into model-agnostic, model-specific, and combination categories.Source: §V · p. 5

A. MODEL-AGNOSTIC

Model-agnostic explainers can be applied across architectures; the review highlights SHAP and LIME alongside related approaches. SHAP is the most-used method in the sample, while LIME examples show explanations can depend on the prediction context.

A. MODEL-AGNOSTIC

1) Shapley Additive Explanations (SHAP).

  • SHAP is a unified feature-importance measure whose stated properties are local accuracy, missingness, and consistency.Source: 1) Shapley Additive Explanations (SHAP) · p. 5
  • SHAP is the most-used method in the sample and appears in anomaly detection, fault diagnosis, and prognosis.Its use across these tasks is attributed as likely to its versatility as a model-agnostic method that can provide global explanations.Source: 1) Shapley Additive Explanations (SHAP) · p. 5
  • In fault diagnosis, SHAP identifies important XGBoost features that are checked against fault reports; another study used SHAP for root-cause analysis of shutdown anomalies.The XGBoost diagnosis framework validates features with reports accompanying faults; the anomaly-detection study found isolation forest best by detected unplanned shutdowns.Source: 1) Shapley Additive Explanations (SHAP) · p. 6

2) Local Interpretable Model-agnostic Explanations (LIME).

3) Feature Importance.

The reviewed XAI methods range from feature-ranking approaches and relevance propagation to rule-based explainers and surrogate models. Some methods embed explanations in model development or training, while others translate model behavior into rules or simpler models.

3) Feature Importance.

  • Feature-importance approaches rank input features by their influence or relevance, using methods including Gini importance, permutation importance, clustering-based selection, and chi-square.Examples also rank time steps by anomaly and use feature importance to verify Tree Interpreter.Source: 3) Feature Importance · p. 7

4) Layer-wise Relevance Propagation (LRP).

  • LRP propagates relevance scores backward from output to input, and one battery-aging approach embedded LRP-derived importance in training to optimize performance.The explainability-driven approach was reported to have superb accuracy compared with a data-driven approach.Source: 4) Layer-wise Relevance Propagation… · p. 7

5) Rule-based Explainers.

  • Rule-based explainers convert model outputs and training data into IF-THEN rules; applications include KPI-based HMM reasoning, temporal logic for failure prediction, and online regression rules for transport faults.The temporal-logic approach was applied to Blackblaze Hard Drive, Tennessee Eastman Process, and CMAPSS datasets and reported great performance with rule-based explanations.Source: 5) Rule-based Explainers · pp. 7–8

6) Surrogate Models.

  • Surrogate approaches use simpler interpretable models to represent black-box behavior; examples include paired ARIMA models, decision-tree fault explanations, and edge-computing diagnosis.The edge-computing study reported that explainable predictive maintenance could theoretically occur on edge devices after hardware and accuracy optimization.Source: 6) Surrogate Models · p. 8

7) Integrated Gradients.

The review covers several explanation approaches in predictive maintenance, from feature attribution and causal analysis to visual, accelerated, and physics-assisted methods. Its examples include specific applications and reported outcomes across these approaches.

7) Integrated Gradients.

  • Gradients through network layers support Integrated Gradients, which attributes deep-model predictions to input features; PredMaX also uses it to identify relevant sensor channels for malfunctioning parts.PredMaX first applies a deep convolutional autoencoder and clusters its latent space to identify channels contributing to normal-to-abnormal transitions.Source: 7) Integrated Gradients · p. 8

8) Causal Inference.

  • A denoising VAE-and-MLP anomaly framework modeled correlation rather than cause-effect relationships, a limitation attributed mainly to limited data availability.The Peter-Clark algorithm was used to examine whether the VAE learned cause-effect relationships.Source: 8) Causal Inference · p. 8

9) Visualization.

  • For bearing diagnosis under unknown working conditions, log-STFT-MSCResNet performed among the best, used few features, and trained faster than the compared models.Its STFT features are visualized for explainability, while MSCResNet enlarges the receptive field without adding parameters.Source: 9) Visualization · pp. 8–9

10) Accelerated Model-agnostic Explanations (ACME).

  • ACME generated explanations much faster using all data, while SHAP was slower even with access to 30% of the data.The comparison applied both methods to anomaly detection on roller-coaster and compacting-machine datasets.Source: 10) Accelerated Model-agnostic… · p. 9

11) Statistics.

  • Physics-assisted kNN and MLP models outperformed their non-assisted counterparts for detecting leak-related faults in vehicle air systems.The models used data generated from three physics equations that modeled air leakage.Source: 11) Statistics · p. 9

12) Smooth Gradients (SmoothGrad).

This review describes gradient-based, counterfactual, and model-specific explanation methods, alongside examples of their use in predictive maintenance. Reported evaluations include comparisons of explanation plausibility and a machining-anomaly pipeline.

12) Smooth Gradients (SmoothGrad).

  • SmoothGrad differentiates the prediction model with respect to its input to create a sensitivity map indicating how input-pixel changes affect classification [156].The map can indicate regions that are key to a prediction.Source: 12) Smooth Gradients (SmoothGrad) · p. 9

13) Counterfactuals.

  • For cold-rolling maintenance, a semi-supervised Physics-Informed Auto-Encoder was more accurate than a base autoencoder, and counterfactuals identified important features in its decisions.The model appends outputs from physics equations to its input data.Source: 13) Counterfactuals · p. 10

14) Explain Like I’m 5 (ELI5).

B. MODEL-SPECIFIC

  • Model-specific methods generate explanations using properties of the architecture being explained, including CAM, GradCAM, and DIFFI.The review contrasts them with model-agnostic approaches in its method categorization.Source: B. MODEL-SPECIFIC · p. 10

1) Class Activation Mapping (CAM) and Gradient-weighted Cam (GradCAM).

  • GradCAM highlighted labeled important features in a CNN anomaly-detection study, while LRP highlighted non-distinguishable features and LIME highlighted unimportant ones.In a separate comparison on predictive-maintenance datasets, GradCAM performed best across the authors’ nine metrics.Source: 1) Class Activation Mapping (CAM) and… · p. 10

2) Depth-based Isolation Forrest Feature Importance (DIFFI).

  • CUAD-MO combined feature extraction, unsupervised FSCA feature selection, Isolation Forest anomaly detection, and DIFFI explanations, achieving 67% precision on two years of CNC data.Its feature extraction included basic statistics and higher-order signal moments such as kurtosis.Source: 2) Depth-based Isolation Forrest… · pp. 10–11

3) LionForests.

The section surveys local and feature-based explanations, anomaly root-cause analysis, combinations of explainers, and intrinsically interpretable models. Its examples include differing explanations from paired methods and an automatic predictive-maintenance workflow.

3) LionForests.

  • LionForests explains random-forest predictions locally through IF-THEN rules and feature-range visualizations, and was expanded for multi-label fault diagnosis,.The expansion offers single-label, predicted-labelset, and label-subset explanation strategies.Source: 3) LionForests · p. 11

4) Saliency Maps.

  • Saliency maps approximate a CNN’s output locally with a linear function, ranking input pixels by their influence on that output [163]..Source: 4) Saliency Maps · p. 11

5) Autoencoder-based Anomaly Root Cause Analysis (ARCANA).

  • ARCANA explains autoencoder reconstruction errors by identifying features associated with them, and its wind-turbine study also found important sensors relevant to known anomalies.The study found the most important feature matched the one with the largest reconstruction error; ARCANA also identified relevant sensors when they did not appear in that error.Source: 5) Autoencoder-based Anomaly Root… · p. 11

C. COMBINATION OF METHODS

  • For RUL predictions, LIME failed to give identical explanations for identical instances, while LIME and SHAP differed across classes; an AutoML workflow applied both explainers to local and whole-model outputs,.TPOT performed best in accuracy in both dataset-subsection experiments.Source: C. COMBINATION OF METHODS · p. 12

VI. INTERPRETABLE ML IN PREDICTIVE MAINTENANCE

  • Interpretable machine-learning models are designed to be understandable without a separate post-hoc explanation method, using human-readable outputs or intelligible structures such as rules and decision trees..Source: §VI · p. 12

A. ATTENTION.

The review presents interpretable predictive-maintenance approaches based on attention, fuzzy logic, and knowledge representations. The examples use these structures for fault diagnosis or prediction and, in some cases, provide explanations through attention, rules, or graph relationships.

A. ATTENTION.

  • Attention supports fault diagnosis by highlighting features or latent-space information, and an anomaly-precursor method’s explanations were verified with domain experts,,.Other reviewed attention-based approaches use anomaly scores over time for fault prediction or combine anomaly detection with anomaly accumulation.Source: A. ATTENTION · p. 12

B. FUZZY-BASED.

  • Fuzzy approaches include transfer learning with fuzzy-rule activation, a five-layer Mamdani neuro-fuzzy model, and a type-2 system optimized for fault prediction,,.An extension of the type-2 system reported that 80% of respondents agreed or strongly agreed that they trusted the interpretable system.Source: B. FUZZY-BASED · pp. 12–13

C. KNOWLEDGE-BASED.

  • Knowledge-based approaches represent feature relationships as links or rules; reviewed examples use a maintenance knowledge graph for fault solutions and IF-THEN rules for diagnosis,.A separate system mines chronicle rules, integrates expert rules, and applies them to semiconductor anomaly prediction.Source: C. KNOWLEDGE-BASED · pp. 13–14

D. INTERPRETABLE FILTERS.

The section surveys interpretable filters, tree-based methods, and physical constraints used to make predictive-maintenance models or their outputs more understandable.

D. INTERPRETABLE FILTERS.

  • CWC uses physically meaningful wavelet filters to make a CNN’s first layer interpretable, while SincNet uses predefined digital filters on raw vibration signals.CWC outperformed a CNN without that layer and learned a well-defined waveform; SincNet had higher precision than a CNN and converged faster.Source: D. INTERPRETABLE FILTERS · p. 14

E. DECISION TREES.

  • Separate decision-tree models performed better than one model across hard-drive RUL and failure-classification tasks, while interpretable methods shared many important features.The experiments covered long- and short-term health, including settings with limited information.Source: E. DECISION TREES · p. 14

F. FAULT TREES.

  • C4.5 with LIFT automates fault-tree construction, while fault-tree traversal can also yield rules modeling how faults develop over time.Experts viewed the heater explanations positively, although the automated method was not optimal because it oversimplified the problem and used a greedy heuristic.Source: F. FAULT TREES · p. 15

G. PHYSICAL CONSTRAINTS.

  • Physical constraints include first-principle models and physics-informed networks that connect predictive outputs or learned patterns to system physics.A valve model accounted for shading-ring degradation and mechanical wear; bearing equations supported interpretable clearance detection, and PCVNN represented learned gear-pump patterns consistently with physics.Source: G. PHYSICAL CONSTRAINTS · p. 15

H. STATISTICAL METHODS.

This section reviews statistical, graph-based, mixture-model, additive, and state-space approaches used in predictive maintenance and fault diagnosis.

H. STATISTICAL METHODS.

  • Yao et al. combine a kurtosis-energy metric, health index, statistical alarms, fault identification, and health-phase analysis; tests on rolling-bearing data reported very low false positives.Their time-frequency analysis suppresses noise and forms sub-bands for monitoring; failure of statistical tests triggers anomaly detection.Source: H. STATISTICAL METHODS · p. 15

I. GRAPH ATTENTION NETWORKS (GATS).

  • Causal-GAT constructs a directed acyclic graph from causal discovery and/or expertise, then uses disentangled causal attention to represent effect variables and classify system status.Its custom loss compares current support of representations with theoretically disentangled support.Source: §I · p. 16

J. GAUSSIAN MIXTURE MODEL.

  • Gaussian mixture models represent feature distributions directly, and Csalodi et al. used them with Weibull survival analysis to model lithium-ion battery health.Their method represented unhealthy-battery distributions more accurately than healthy-battery distributions, whose larger category was harder to represent with one small model.Source: J. GAUSSIAN MIXTURE MODEL · p. 17

K. EXPLAINABLE BOOSTING MACHINE (EBM).

  • Explainable boosting machines are additive models whose learned feature functions and selected feature interactions can be explained through their impacts on the outcome.The passage describes EBM as a glassbox model with accuracy similar to state-of-the-art black-box algorithms.Source: K. EXPLAINABLE BOOSTING MACHINE (EBM) · p. 17

L. HIDDEN MARKOV MODEL.

  • An input-output HMM identifies failure states, after which a reinforcement-learning agent learns a maintenance policy using hold, repair, or replace actions.The HMM supports interpretation by exposing features that led to failure-state detection; rewards encode holding and replacement costs.Source: L. HIDDEN MARKOV MODEL · p. 17

M. SPARSE NETWORKS.

The section covers sparse models, prototypes, temporal logic, digital twins, and symbolic life models as interpretable predictive-maintenance approaches.

M. SPARSE NETWORKS.

  • A two-layer network using restricted sparse frequency-domain features achieved performance equal to CNN-LSTM with less memory and CPU usage, while other sparse models emphasized simplicity or feature selection.The cited approaches include a failure score combining a gradient-boosting regressor, isolation forest, and mean temperature, and elastic-net logistic regression for anomaly prediction.Source: M. SPARSE NETWORKS · p. 17

N. PROTOTYPE LEARNING.

  • ProSeNet predicts fault classes from diagnostic trouble codes using similarities between encoded sequences and prototypes, and human feedback improved interpretability in a user study.Its recurrent sequence encoder feeds a prototype layer whose similarity vector informs class probabilities.Source: N. PROTOTYPE LEARNING · p. 18

O. SIGNAL TEMPORAL LOGIC (STL).

  • Signal temporal logic expresses predicates over dense-time real-valued signals, and reinforcement learning can search for an optimal STL formula for furnace fault diagnosis.The furnace study reported robustness, fast runtimes, and statistically significant performance across multiple faults.Source: O. SIGNAL TEMPORAL LOGIC (STL) · p. 18

P. DIGITAL TWIN.

  • A conveyor digital twin compares simulated sensor data with real-time data and lets users rate explanations, with further simulations used when an explanation is judged invalid.The twin displays system information and supports user input on explanation validity.Source: P. DIGITAL TWIN · p. 18

Q. SYMBOLIC LIFE MODEL.

  • DSASA combines genetic-programming symbolic life models with dynamic adjustment using real-time performance to produce improved models for RUL prediction.Its models are described as interpretable because they are simple and operate based on physical constraints.Source: Q. SYMBOLIC LIFE MODEL · p. 18

R. GENERALIZED ADDITIVE MODEL (GAM).

The section surveys additive and distance-based models, rule-based interpretations, and challenges in designing explanations for predictive-maintenance stakeholders.

R. GENERALIZED ADDITIVE MODEL (GAM).

  • A NASGP-based interpretable GAM using additive kernels and individual features performed well against other methods on IEEE PHM 2012 RUL-prediction and fault-diagnosis tasks.GAMs estimate outcomes by summing smoothed nonlinear local models trained on individual features, whose impacts can be interpreted.Source: R. GENERALIZED ADDITIVE MODEL (GAM) · pp. 18–19

S. MAHALANOBIS-TAGUCHI SYSTEM (MTS).

  • MTS diagnoses through Mahalanobis distance from stable operation, using orthogonal arrays and signal-to-noise ratios to identify responsible variables; its distance-based discrimination requires distinguishable classes.A cited fault-detection application detected roughly 75% of tested faults.Source: S. MAHALANOBIS-TAGUCHI SYSTEM (MTS) · p. 19
  • A modified kNN method addresses sparse regions, class-boundary blindness, and class overlap through local similarity and neighborhood homogeneity, with classes visualized on a low-dimensional graph.The method was used to generate decision support for temperature alarms.Source: T. K-NEAREST NEIGHBORS (KNN) · p. 19

U. RULE-BASED INTERPRETATIONS.

  • CAP combines case-crossover design with Apriori mining to extract additive and subtractive rules around transitions from healthy operation to failure, and outperformed random forest on the same problem.The design uses the period before class change as control and moments closer to the change as the case period.Source: U. RULE-BASED INTERPRETATIONS · p. 19

VII. CHALLENGES AND RESEARCH DIRECTIONS OF EXPLAINABLE PREDICTIVE MAINTENANCE

  • The survey identifies underrepresented facets beyond adding explainability to complex predictive-maintenance problems, including root-cause analysis and fault validation.Researchers have used XAI and interpretable ML for those purposes, but the section says other facets generally receive less attention.Source: §VII · p. 19

A. PURPOSE OF THE EXPLANATIONS

  • Explanations often lack a specified audience, although data scientists, project managers, stakeholders, and mechanics may need different levels of physical, temporal, or abstract information.The survey notes that explanations are frequently designed around the model rather than stakeholders.Source: A. PURPOSE OF THE EXPLANATIONS · pp. 19–20

B. EVALUATION OF THE EXPLANATIONS

The review highlights limited evaluation of explanations in predictive maintenance and recommends involving intended users in explanation evaluation. It also notes that its literature coverage is selective and synthesizes method categories, evaluation metrics, and human-centered directions.

B. EVALUATION OF THE EXPLANATIONS

  • Explanation evaluation has received less attention than algorithm-performance evaluation, despite prior work cataloguing 37 effectiveness metrics and 28 evaluation metrics.The cited work also covers human-centered and objective measures, including user comprehension, trust, and explanation properties.Source: B. EVALUATION OF THE EXPLANATIONS · p. 20

C. ADDITION OF HUMAN INVOLVEMENT

  • Researchers should identify the target audience and use a statistically significant sample to gather feedback, supporting quality metrics and customizable explanations.The authors frame this as a route toward human-AI teaming in predictive maintenance.Source: C. ADDITION OF HUMAN INVOLVEMENT · pp. 20–21

D. STUDY LIMITATIONS

  • The survey covers only a small portion of potential XAI and iML literature and omits some popular methods and applicable predictive-maintenance algorithms.Source: D. STUDY LIMITATIONS · p. 21

VIII. CONCLUSION

  • The review groups XAI methods as model-agnostic or model-specific and distinguishes them from iML approaches using inherently interpretable models.It identifies underuse of explanation metrics in predictive maintenance and proposes human feedback after defining and sampling the target audience.Source: §VIII · p. 21

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