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Condition-based maintenance programs for modern helicopters rely on algorithmic techniques to estimate the useful life remaining for life-limited components. Regime-recognition-based condition-based maintenance programs involve a regime recognition step and a damage estimation step in which damage is calculated based on the identified regimes. Recently, new probabilistic regime recognition algorithms have been developed that produce probability distributions over the regimes, rather than deterministic regime classifications. However, to date, there has been no method to convert regime distributions to damage estimates. This paper proposes a technique to compute a probability distribution over the fatigue damage for each life-limited component directly from the regime probability distributions. The method treats the incurred damage at a given time as a random variable and accumulates the total damage incurred as a sum of random variables. The damage distribution at each time is computed from the regime distribution and the regime damage rates. A primary advantage of the approach is that it captures uncertainty in the regime recognition process by treating damage as a random variable rather than a deterministic value. Simulation results illustrate the benefit of the probabilistic approach over a deterministic method, particularly for flights where there is significant uncertainty in the flown regimes.

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Helicopters are extensively used in civil applications as they are versatile in their capabilities to manoeuvre. Their operation under harsh conditions and environments demand for a strict maintenance plan. Main gearboxes (MGB) of helicopters are a critical component responsible for reducing the high input speed generated from the gas turbine engines. Health and Usage Monitoring Systems (HUMS) are installed in an effort to monitor the health state of the transmission systems, and ideally, to detect and diagnose the type of a generated fault. Even though the development of HUMS contributed to the reduction of worldwide helicopter accident rate, more advanced systems are needed based on the investigation of the air accidents of AS332 L2 Super Puma in Scotland in 2009 and of EC225 LP Super Puma in Bergen in 2016, due to failure of a planet gear of the MGB. A plethora of signal processing methodologies have been proposed for the early detection of faults but often they fail in complex structures, such as planetary gearboxes operating under various conditions. In this paper the performance of a recently proposed diagnostic tool, called IESFOgram, is evaluated and compared with state of the art techniques, applied on signal captured on a Category A Super Puma SA330 MGB.

Current airframe health monitoring generally relies on deterministic physics models and ground inspections. This paper uses the concept of a dynamic Bayesian network to build a versatile probabilistic model for diagnosis and prognosis in order to realize the digital twin vision, and it illustrates the proposed method by an aircraft wing fatigue crack growth example. The dynamic Bayesian network integrates physics models and various aleatory (random) and epistemic (lack of knowledge) uncertainty sources in crack growth prediction. In diagnosis, the dynamic Bayesian network is used to track the evolution of the time-dependent variables and calibrate the time-independent variables; in prognosis, the dynamic Bayesian network is used for probabilistic prediction of crack growth in the future. This paper also proposes a modification to the dynamic Bayesian network structure, which does not affect the diagnosis results but reduces the time cost significantly by avoiding Bayesian updating with load data. By using a particle filter as the Bayesian inference algorithm for the dynamic Bayesian network, the proposed approach handles both discrete and continuous variables of various distribution types, as well as nonlinear relationships between nodes. Challenges in implementing the particle filter in the dynamic Bayesian network, where 1) both dynamic and static nodes exist and 2) a state variable may have parent nodes across two adjacent networks, are also resolved. © 2016 by the American Institute of Aeronautics and Astronautics, Inc.

Usage monitoring entails determining the actual usage of a component on the aircraft and requires accurate recognition of regimes. In this paper, a data mining approach is adopted for regime recognition. In particular, a regime recognition algorithm developed based on hidden Markov models is presented. The developed algorithm was validated using the flight card data of an Army UH-60L helicopter. The performance of this regime recognition algorithm was also compared with other data mining methods using the same dataset. Using the flight card information and regime definitions, a dataset of about 56,000 data points labeled with 50 regimes recorded in the flight card were mapped to the health and usage monitoring parameters. The validation and performance comparison results have showed that the hidden Markov model based regime recognition algorithm was able to accurately recognize the regimes recorded in the flight card data and outperformed other data mining methods.

We present a new supervised learning procedure for systems composed of many separate networks, each of which learns to handle a subset of the complete set of training cases. The new procedure can be viewed either as a modular version of a multilayer supervised network, or as an associative version of competitive learning. It therefore provides a new link between these two apparently different approaches. We demonstrate that the learning procedure divides up a vowel discrimination task into appropriate subtasks, each of which can be solved by a very simple expert network.

In this paper, a data mining approach is adopted for regime recognition. In particular, a regime recognition algorithm developed based on HMM was presented. The HMM based regime recognition involves two major stages: model learning process and model testing process. The learning process could be implemented off-board. In this process, Gaussian mixture model (GMM) was used instead of unimodal density of Gaussian distribution in HMM. Once the learning process is completed, new incoming unknown signal could be tested and recognized on-board. The developed algorithm was validated using the flight card data of an Army UH-60L helicopter. The performance of this regime recognition algorithm was also compared with other data mining approaches using the same dataset. Using the flight card information and regime definitions, a dataset of about 56,000 data points labeled with 50 regimes recorded in the flight card were mapped to the health and usage monitoring parameters. The validation and performance comparison results have showed that the hidden Markov model based regime recognition algorithm was able to accurately recognize the regimes recorded in the flight card data and outperformed other data mining methods.

The safe operation of helicopters requires that the fatigue lives of dynamic components meet a minimum level of reliability. To estimate the safe operational time of such components a deterministic safety factor approach such as mu plus/minus 3sigma has been widely used by some helicopter manufacturers to determine the retirement lifetime of a component and has been claimed to meet a reliability level of 0.999,999 (six-nines). Based on field experience, this approach has performed well enough to ensure component failures due to fatigue are extremely remote, i.e. a reliability of six-nines appears to have been met. However, the TOS/(mu-3sigma) approach has recently been shown, through theoretical analysis, to be highly non-conservative in estimating the component lifetime at a reliability level of six-nines. To satisfy certification and airworthiness requirements for present and future aircraft structural components there is a need to resolve the discrepancy between the results of theoretical analysis and field experience. In this paper, the source of this discrepancy is identified and methods to address it are discussed.

This paper describes the use of neural networks for near-optimal
helicopter flight load synthesis (FLS), which is the process of
estimating mechanical loads during helicopter flight, using cockpit
measurements. First, modular neural networks are used to develop
statistical signal models of the cockpit measurements as a function of
the loads. Then Cramer-Rao maximum a-posteriori bounds on the
mean-squared error are calculated. Then, multilayer perceptrons for FLS
are designed which approximately attain the bounds. It is shown that all
of the FLS networks have good generalization

This paper describes a novel approach to regime recognition based on the notion of motion primitives. Originally developed for path planning, motion primitives decompose a vehicle trajectory into maneuver and trim segments. In a regime recognition context, this decomposition can be used to improve component life tracking through separate classification of trim segments and maneuver segments. The proposed algorithm functions in three major steps. The first step consists of classifying the flight data into trim and maneuver segments. The second step leverages the information in the trim state and control vectors to classify each trim segment as a particular trim regime based on conditional logic. The final step makes use of dynamic time warping for the classification of each maneuver segment (flown between two trim segments) as a particular maneuver regime. Accuracy of the proposed algorithm is evaluated using simulated flight data for the SH-60B, and advantages of the proposed method compared to a threshold-based algorithm are assessed. The algorithm is also applied to actual flight data from a generic utility helicopter to demonstrate operation of the algorithm using real-world data.

We bound the variance and other moments of a random vector based on the range of its realizations, thus generalizing inequalities of Popoviciu and of Bhatia and Davis concerning measures on the line to several dimensions. This is done using convex duality and (infinite-dimensional) linear programming. The following consequence of our bounds exhibits symmetry breaking, provides a new proof of Jung’s theorem, and turns out to have applications to the aggregation dynamics modelling attractive–repulsive interactions: among probability measures on [Formula: see text] whose support has diameter at most [Formula: see text], we show that the variance around the mean is maximized precisely by those measures that assign mass [Formula: see text] to each vertex of a standard simplex. For [Formula: see text], the [Formula: see text] th moment—optimally centered—is maximized by the same measures among those satisfying the diameter constraint.

Regime recognition (RR) is an important aspect of condition-based maintenance for modern helicopters. RR involves the postflight classification of flight data into regime categories. These classifications are then used to predict fatigue damage and vehicle usage spectra. Although several RR algorithms have been proposed to date, many suffer from an overreliance on training data or poor accuracy when presented with flight data that do not precisely match one of the defined regimes. This paper introduces a new type of RR algorithm based on interacting multiple model (IMM) estimators. IMM estimators use a bank of dynamic models to evaluate the probability of the system existing in one of various possible dynamic modes. In the RR context, each of the dynamic modes corresponds to a particular regime. The proposed recognition algorithm offers advantages over other methods in that it provides a probabilistic classification of flight data, thereby explicitly acknowledging uncertainty in the recognition process. Furthermore, the algorithm is model based, reducing reliance on training data. Following a detailed description of the methodology, results are provided by applying the algorithm to both simulated and actual flight test data. Results show significant performance improvements compared with a typical rule-based recognition scheme.

Regime recognition is a critical tool used for condition-based maintenance, fatigue life prediction, and creation of usage spectra for military and commercial rotorcraft. While a variety of regime recognition algorithms are currently in use, many current algorithms suffer from an over-reliance on training data or poor classification accuracy with respect to the stringent guidelines outlined in ADS-79E. This paper introduces a new type of regime recognition algorithm based on a multiple model adaptive estimation scheme, known as an interacting multiple model (IMM) estimator. IMM estimators use a bank of dynamic models to evaluate the likelihood of the system existing in one of various possible dynamic modes. In the regime recognition context, each mode represents the system operating in a given maneuver regime. Compared with other approaches, IMM estimators offer the benefits of probabilistic regime classification and the incorporation of knowledge of the aircraft flight dynamics, which reduces reliance on training data. This paper presents a novel formulation of an IMM estimator for regime recognition wherein mode probabilities from a bank of IMM filters are combined in Bayesian framework to yield maneuver regime probabilities. Example results for the SH-60B show favorable classification performance in preliminary simulation studies using common maneuvers.

This paper presents a new approach to develop digital twins of helicopter dynamic systems. Helicopter industries attach growing attention to the development of digital twins to be more predictive of mechanical parts lifetime. The number of sensors available to measure loads during flights is limited. Complementary simulations are necessary to compute all the loads that the mechanical parts undergo. A new process is described to build these simulations fed with flights data records. Complexity of helicopters dynamics systems leads to create several local models of subsystems using a multibody dynamic formalism. A study focused on a swashplate rotor assembly is presented to illustrate this approach, including a new model of bearing and its validation based on bench tests.

In this note, we derive upper bounds on the variance of a mixed random variable. Our results are an extension of previous results for unimodal and symmetric random variables. The novelty of our findings is that this mixed random variable does not necessary need to be symmetric and is multimodal. We also characterize the cases when these bounds are optimal.

Regime recognition is an important tool in the creation of usage spectra and component lifetime prediction. During development of regime recognition codes, it is necessary to establish baseline performance using scripted flight-test data. Various problems arise when using scripted flight data for verification and validation that may be mitigated by using simulated data. This paper presents a virtual pilot algorithm designed to generate scripted flight-test data from a helicopter simulator. The virtual pilot receives a maneuver script as input and streams control inputs to a flight simulator to perform the required maneuvers in an accurate and reliable manner. The algorithm is formulated as a variable structure controller where each maneuver is mapped to a single feedback law. Several techniques are employed to validate the virtual pilot approach, and results show that synthetic Health and Usage Monitoring data generated by the virtual pilot compare favorably against actual flight data.

Accurate estimation of helicopter component loads is an important goal for life cycle management and life extension efforts. In this research, estimates of helicopter dynamic loads were achieved through a combination of statistical and machine learning (computational intelligence) techniques. Estimates for the main rotor normal bending (MRNBX) loads on the Sikorsky S-70A-9 Black Hawk helicopter during two flight conditions (full speed forward level flight and rolling left pullout at 1.5g) were generated from an input set comprising 30 standard flight state and control system (FSCS) parameters. Data exploration using principal component analysis and multi-objective optimization of Gamma test parameters generated reduced subsets of predictors. These subsets were used to estimate MRNBX using neural network models trained by deterministic and evolutionary computation techniques. Reasonably accurate and correlated models were obtained using the subsets of the multi-objective optimization, also allowing some insight into the relationship between MRNBX and the 30 FSCS parameters.

A gap in the proof of a non-stationary mixingale invariance principle is identified and fixed by introducing a skipped subsampling of a partial sum process and letting the skipped interval vanish asymptotically at an appropriate rate as the sample size increases. The corrected proof produces a mixingale limit theorem in the form of a mixing convergence in law, occuring jointly with the stable convergence in law for the same σ-field relative to which they are stable and mixing. The applicability of established results to a high-frequency estimation of the quadratic variation of financial price process is discussed.

Several U.S. Navy rotorcraft models are equipped with Health and Usage Monitoring Systems. On-board or on-ground Regime Recognition (RR) programs are used to develop individual rotorcraft usage spectrums to compute component and airframe fatigue life expended (FLE). FLE is a function of rotorcraft gross weight (GW) and center of gravity (CG), but neither are monitored by sensors. Thus GW and CG computation algorithms based on measured engine torque curves and trim equations during hover are developed and incorporated into RR. The algorithms are validated using numerous fleet flights with known GWs and CG positions. Excellent correlation between predicted and actual values is observed with low standard error of estimate. The in-flight variation of GW and CG is determined with the help of recorded fuel weight. RR is used to analyze 32,000 h of data from 111 rotorcraft to develop GW and CG utilization distributions. Furthermore, GW variation is modeled with a beta probability distribution and the joint probability distribution of GW and CG utilization is determined to assess airframe and dynamic component fatigue lives.

A new approach to flight control system design is presented which takes into account the operational usage (condition) of the helicopter. The flight control system gains are scheduled as a function of the condition of the helicopter, provided by the health and usage monitoring system. As a result, the utilization rate of the helicopter can be increased and maintenance costs can be reduced. The approach is demonstrated for vertical axis control of the Bell 412 helicopter operating at low speed. The control system is designed to provide a height rate response type combined with torque limit protection. For low to high levels of aggressiveness, level 1 handling qualities are achieved in piloted simulation of a bob-up maneuver compared to level 2 for the original aircraft without a vertical axis control law. The control system successfully prevents the torque from exceeding the limit. Two conditions are defined, based on which the control system gains are scheduled. The first condition is the number of transmission limit exceedances and the second is the number of rapid torque excursions. Four different control modes are possible due to these conditions. For implementation of this specific control law on a real-life aircraft, emergency situations must be considered in which the pilot needs to exceed the torque limit of the aircraft intentionally to ensure safety. This can be achieved through a tactile cueing system.

A neural network model is developed to predict selected rotor system vibratory loads of an H-60 helicopter. The load model is based on input parameters which can be readily measured and recorded in the fuselage using a flight data recorder. The model has been developed using flight test data from a highly instrumented SH-60B aircraft which included a slipring assembly and strain gauges mounted in the rotating system. The strain gauge measurements provide a reference vibratory load for neural network model correlation. Load models are also assessed on flight test data from a second H-60 aircraft which was also instrumented with strain gauges in the rotating system. Two types of neural network algorithms are used in the analysis. A self organizing feature map algorithm is used for training data set selection and a modular neural network algorithm is used for load predictions. Predicted loads compare quite well with strain gauge measurements and results show that the load models provide good correlation on test data from the second H-60 aircraft.

Future generations of NASA and U.S. Air Force vehicles will require lighter mass while being subjected to higher loads and more extreme service conditions over longer time periods than the present generation. Current approaches for certification, fleet management and sustainment are largely based on statistical distributions of material properties, heuristic design philosophies, physical testing and assumed similitude between testing and operational conditions and will likely be unable to address these extreme requirements. To address the shortcomings of conventional approaches, a fundamental paradigm shift is needed. This paradigm shift, the Digital Twin, integrates ultra-high fidelity simulation with the vehicle's on-board integrated vehicle health management system, maintenance history and all available historical and fleet data to mirror the life of its flying twin and enable unprecedented levels of safety and reliability.

The Navy has been developing its flight usage survey and structural monitoring capabilities for helicopter applications for many years. This paper describes the development and verification process used to establish structural usage monitoring capability for the H-60 series helicopter models presently in the Navy inventory. The paper discusses the approach used to acquire and establish a database of known flight maneuver data for the aircraft. The process of developing maneuver recognition criteria using the flight test database is described along with a discussion of the verification process used to substantiate the maneuver recognition logic and software. The paper presents some examples of the methods used in processing the flight test data to develop and define selected maneuver recognition criteria and parameter thresholds. The paper also includes a discussion of some of the problems, limitations and issues related to maneuver recognition criteria development and verification. Selected maneuver examples are used to illustrate some of the difficulties in maneuver identification. The paper concludes with some recommendations with regard to the development and verification of maneuver recognition criteria for application to other models.

Multiple regression analysis of helicopter flight data is used to develop prediction models for rotating system component loads from parameters measured in the fixed system. The data base that is analyzed contains load measurements for a helicopter performing several types of flight maneuvers, including symmetric pullouts, rolling pullouts, climbing turns, and level flight. The data are divided into two parts: one for model development and one to serve as a blind test of the model. For steady level flight, linear and nonlinear regression analyses are performed to predict main rotor pushrod and blade normal bending vibratory loads. Correlations above 95% were achieved on the test data for the steady level flight condition. For comparison, analytical results calculated using the CAMRAD/JA rotor analysis computer code for the helicopter in level flight are included. Regression models to predict vibratory loads during maneuvering flight are also developed. Evaluations on the test data indicate that correlations ranging from 79 to 95% are possible for the types of maneuvers contained in the data base.

The fatigue life of dynamic helicopter components is highly dependent on the history of loads experienced by the components during flight. However, practical methods of monitoring the loads on individual components during flight have not been developed. Current maintenance programs are characterized by frequent inspections and sometimes premature retirement of safety-critical components. This paper proposes using an artificial neural network (ANN) to predict the loads in critical components based on flight variable information that can be easily measured. The artificial neural network learns the relationship between flight variables and component loads through exposure to a database of flight variable records and corresponding load histories taken from an instrumented military helicopter undergoing standard maneuvers. Eight standard flight variables are used as inputs for predicting the time-varying mean and oscillatory components of the tailboom bending load and the pitch link load for seven flight maneuvers. The ANN predicts the mean and oscillatory components with accuracy ranging from 90.70% to 97.7% correct.

The perceived benefits of permanent usage monitoring equipment in helicopters include savings in the cost of helicopter maintenance and a favourable impact on safety and fleet management. Unlike indirect fatigue monitoring, direct load monitoring relies on a large number of sensors which requires high operational and maintenance costs. In this paper, a learning network has been developed, and during training sessions allowed to learn how to predict fatigue damage indirectly from flight parameters. Each training example consists of instantaneous fatigue damage induced during a small time step, and flight parameters measured during the time step. The instantaneous damage values are evaluated through a new approach called the progressive damage model. By considering the laws of aerodynamics and dynamics, the network combines the flight parameters in such a way that the resulting features can be mapped into fatigue. About 10.5 flying hours of data were used to train the network. After training, the network was blind tested using flight parameters from 5.8 flying hours. The network was found to predict the fatigue damage of two rotating components indirectly from the flight parameters with accuracy better than the accuracy of a strain gauge system with 5 per cent measurement error.

There is great concern in the U. S. Navy/Marine Corps aviation community regarding out-year operating costs. Simply put, there may not be sufficient funds for the services to execute their mission goals. Studies and initiatives have been undertaken to reduce Operational and Support Costs, with a keen interest in Condition Based Maintenance (CBM) and a re-structuring of the logistics infrastructure. A key artifact of CBM, Structural Health and Usage Monitoring (SHUM), is vital to the Chief of Naval Operations (CNO) vision of "the right readiness, at the right cost." The Structural Appraisal of Fatigue Effects (SAFE) program at the Naval Air Systems Command (NAVAIR) has been providing structural tracking information to maintain the structural integrity of US Navy aircraft for over 30 years. The SAFE program uses parametric data from onboard flight recorders to accrue component life consumption via actual flight data vice an assumed usage spectrum. The objective is to determine if an aircraft is flown more or less severely than designed, and to provide benefit in the form of either safety or economy. Although most of the beneficiaries from the SAFE program have been fixed wing aircraft, NAVAIR has been working to implement the first rotorcraft fleet in SAFE, the Integrated Mechanical Diagnostics System (IMDS) equipped CH-53E helicopter. Seven CH-53E components selected upon criticality, perceived benefit, and expense, were evaluated via SAFE. There are two ways to execute SHUM. The first is to implement a CH-53E SAFE program to provide a Fatigue Life Expended (FLE) metric based upon component specific aircraft usage. The second is to update the aircraft usage spectrum based upon fleet-wide aircraft usage. The CH-53E program has funded both of these paths to maximize benefit.

Fatigue life estimation of helicopter dynamic components is a complex process that is currently achieved through many different methods. The objective of this study was to review existing methods and to develop a standardized method that could be used by the Army for reliably predicting operational life. This report presents results of a detailed review of fatigue life methods used by five helicopter manufacturers as determined by site visits and literature reviews. Recommendations for a standardized method are presented in areas of mission spectra definition, flight strain survey techniques, laboratory fatigue strength characterization, and safe-life calculation procedures.

The U. S. Navy has developed a usage monitoring system based on the regime recognition concept for tracking rotary wing aircraft fatigue components and structures. Thus far, 50 AH-1W aircraft have been equipped with the Structural Data Recording Set (SDRS), acquiring 3400 valid flight hours of usage. The usage variations in each regime are modeled using a Weibull distribution. Similarly, the load variations in each regime are also modeled using a Weibull distribution. The strength variation was obtained from the aluminum alloy-264 full-scale component fatigue test data. This variation is modeled using a Weibull distribution. The usage, load, and strength variations are then combined to compute fatigue life and the associated multivariate probability of failure and reliability. The component fatigue lives versus the reliability curve will help the U. S. Navy plan component retirements with specified risks. In addition, the individual contribution from usage, loads, strength, and cycle counting to six nines reliability are calculated. Finally, the impact of usage monitoring on reliability is assessed and the bivariate standard deviation required to achieve six nines reliability is evaluated.

In the past 15 years, the Navy has conducted a number of different usage surveys for helicopter models, such as AH-1W, H-46, H-60, and H-3, in an effort to better define fleet usage and to develop accurate usage spectra for each model. The surveys were conducted with various structural usage monitoring systems (SUMSs), such as onboard regime recognition, flight parameter recording, and limited flight parameter recording with a low-cost usage monitoring system. The number of aircraft involved in the survey was 50, 20, 10, and 7 for the AH-1W, H-46, H-60, and H-3, respectively. The surveys ranged in duration from months to years. This paper presents an innovative technique to use in data recording, sampling, RAM, and storage memory for various monitoring systems and the systematic approach of usage spectrum development using statistical cumulative frequency distribution of usages. The sensitivity of usage spectrum on rotating component fatigue life is studied and used in the usage spectrum refinement. Further optimization of the usage spectrum is carried out with respect to cycle counting and prorating of angle of bank, altitude, velocity, and gross weight. In addition, the contribution of usage spectrum to reliability of computed retirement life is studied. The usage spectra developed using SUMSs are compared with design, operational, and classical AR-56 spectra for various classes of helicopters. The present analysis leads to the conclusion that additional usage monitoring should be conducted to enhance the database, aid in refinement of AR-56 spectra to reflect the actual modern fleet utilization of Navy helicopters, and update associated requirements. Individual helicopter usage monitoring is essential to enhance flight safety and to identify possible logistics cost savings.

A flight loads variability analysis program was conducted using the Bell Model OH-58C helicopter. A representative flight consisting of 33 maneuvers was repeated 30 times using six pilots (three from Bell Helicopter Textron and three from the Army) who flew the aircraft five times each. The resulting data were analyzed statistically to determine the parameters of distribution and variability using three different sets of data: peak loads, maneuver loads and total flight loads. In addition, the damage rates were also analyzed statistically. The results indicate that the maximum oscillatory loads exhibit a larger variability than that obtained by analyzing either maneuver loads or the flight loads and that the Weibull distribution can be used to represent the distribution shapes of both the maneuver and flight loads. Assessment of load variability on a total flight basis reduces the complexity of reliability computations.

A neural network for the prediction of oscillatory loads used for on-line health monitoring of flight critical components in an AH-64A helicopter is described. The neural network is used to demonstrate the potential for estimating loads in the rotor system from fixed-system information. Estimates of the range of the pitch link load are determined by the neural network from roll, pitch, and yaw rates, airspeed, and other fixed-system information measured by the flight control computer on the helicopter. The predicted load range is then used to estimate fatigue damage to the pitch link. Actual flight loads data from an AH-64A helicopter are used to demonstrate the process. The predicted load ranges agree well with measured values for both training and test data. A linear model is also used to predict the load ranges, and its accuracy is noticeably worse than that of the neural network, especially at higher load values that cause fatigue damage. This demonstrates the necessity of the non-linear modelling capabilities of the neural network for this problem.

In this paper the central limit problem is solved for sums of random variables having bounded variances and satisfying certain mixing conditions. In case of a stochastic process these mixing conditions essentially say that as time passes events concerning the future of the process are almost independent from the events in the past. It turns out that the class of limit laws for sums of mixing random variables is exactly the same as for the bounded variances case of independent random variables. We also shall give criteria for convergence to any specified law of this class of possible limit laws. Finally we shall derive the central limit theorem involving a kind of Lindeberg-Feller condition and as a corollary thereof a kind of Ljapounov theorem.

We prove a functional central limit theorem for a class of strongly mixing sequences of random variables. Stationarity is not assumed, but the variances of the partial sums must grow linearly. Our theorem extends previous results by supplying sufficient conditions for the weak convergence of the partial sum process to the Wiener process under less restrictive moment assumptions. For instance, if
supn \text EXn2 |log|Xn ||1 + e < ¥\mathop {\sup }\limits_n {\text{ }}EX_n^2 |\log |X_n \parallel ^{1 + \varepsilon } < \infty
for some >0, and the mixing rate is exponential, then this functional c.l.t. holds. Under the weaker assumption with =0, the c.l.t. may fail to hold, and it is possible that the c.l.t. is satisfied, but the sequence of partial sum processes is not tight.

Considerations on stochastic models frequently involve sums of dependent random variables (rv's). In many such cases, it is worthwhile to know if asymptotic normality holds. If so, inference might be put on a nonparametric basis, or the asymptotic properties of a test might become more easily evaluated for certain alternatives. Of particular interest, for example, is the question of when a weakly stationary sequence of rv's possesses the central limit property, by which is meant that the sum $\sum^n_1 X_i$, suitably normed, is asymptotically normal in distribution. The feeling of many experimenters that the normal approximation is valid in situations "where a stationary process has been observed during a time interval long compared to time lags for which correlation is appreciable" has been discussed by Grenander and Rosenblatt ([10]; 181). (See Section 5 for definitions of stationarity.) The general class of sequences $\{X_i\}_{-\infty}^\infty$ considered in this paper is that whose members satisfy the variance condition \begin{equation*}\tag{1.1}\operatorname{Var} (\sum^{a+n}_{a+1} X_i) \sim nA^2\text{uniformly in} a (n \rightarrow \infty) (A^2 > 0).\end{equation*} Included in this class are the weakly stationary sequences for which the covariances $r_j$ have convergent sum $\sum_1^\infty r_j$. A familiar example is a sequence of mutually orthogonal rv's having common mean and common variance. As a mathematical convenience, it shall be assumed (without loss of generality) that the sequences $\{X_i\}$ under consideration satisfy $E(X_i) \equiv 0$, for the sequences $\{X_i\}$ and $\{X_i - E(X_i)\}$ are interchangeable as far as concerns the question of asymptotic normality under the assumption (1.1). As a practical convenience, it shall be assumed for each sequence $\{X_i\}$ that the absolute central moments $E|X_i - E(X_i)|^\nu$ are bounded uniformly in $i$ for some $\nu > 2$ ($\nu$ may depend upon the sequence). When (1.1) holds, this is a mild additional restriction and a typical criterion for verifying a Lindeberg restriction ([15]; 295). We shall therefore confine attention to sequences $\{X_i\}$ which satisfy the following basic assumptions (A): \begin{equation*}\tag{A1}E(X_i) \equiv 0,\end{equation*}\begin{equation*}\tag{A2}E(T_a^2) \sim A^2 \text{uniformly in} a (n \rightarrow \infty) (A^2 > 0),\end{equation*}\begin{equation*}\tag{A3}E|X_i|^{2+\delta} \leqq M (\text{for some} \delta > 0 \text{and} M < \infty),\end{equation*} where $T_a$ denotes the normed sum $n^{-\frac{1}{2}} \sum^{a+n}_{a+1} X_i$. Note that the formulations of (A2) and (A3) presuppose (A1). We shall say, under assumptions (A), that a sequence $\{ X_i\}$ has the central limit property (clp), or that $T_1$ is asymptotically normal (with mean zero and variance $A^2$), if \begin{equation*}\tag{1.2}P\{(nA^2)^{-\frac{1}{2}}\sum^n_1 X_i \leqq z\} \rightarrow (2\pi)^{-\frac{1}{2}} \int^z_{-\infty} e^{-\frac{1}{2}t{}^2}dt\quad (n \rightarrow \infty).\end{equation*} The assumptions (A) do not in general suffice for (1.2) to hold. (The reader is referred to Grenander and Rosenblatt ([10]; 180) for examples in which (1.2) does not hold under assumptions (A), one case being a certain strictly stationary sequence of uncorrelated rv's, another case being a certain bounded sequence of uncorrelated rv's.) It is well known, however, that in the case of independent $X_i$'s the assumptions (A) suffice for (1.2) to hold. It is desirable to know in what ways the assumption of independence may be relaxed, retaining assumptions (A), without sacrificing (1.2). Investigators have weakened considerably the moment requirements (A2) and (A3) while retaining strong restrictions on the dependence. However, in many situations of practical interest, assumptions (A) hold but neither strong dependence restrictions nor strong stationarity restrictions seem to apply. Thus it is important to have theorems which take advantage of assumptions (A) when they hold, in order to utilize conclusion (1.2) without recourse to severe additional assumptions. A basic theorem in this regard is offered in Section 4. It is unfortunate that the additional assumptions required, while relatively mild, are not particularly amenable to verification, with present theory. This difficulty is alleviated somewhat by the strong intuitive appeal of the conditions. The variety of ways in which the assumption of independence may be relaxed in itself poses a problem. It is difficult to compare the results of sundry investigations in central limit theory because of the ad hoc nature of the suppositions made in each instance. In Section 2 we explore the relationships among certain alternative dependence restrictions, some introduced in the present paper and some already in the literature. Conditions involving the moments of sums $\sum^{a+n}_{a+1} X_i$ are treated in detail in Section 3. The central limit theorems available for sums of dependent rv's embrace diverse areas of application. The results of Bernstein [2] and Loeve [14], [15] have limited applicability within the class of sequences satisfying assumptions (A). A result that is apropos is one of Hoeffding and Robbins [11] for $m$-dependent sequences (defined in Section 2). In addition to assumptions (A1) and (A3), their theorem requires that, defining $A_a^2 = E(X^2_{a+m}) + 2 \sum^m_1E(X_{a+m-j}X_{a+m},$ \begin{equation*}\tag{H}\lim_{n\rightarrow\infty} n^{-1}\sum^n_{i = 1} A^2_{a+i} = A^2 \text{exists uniformly in} a (n \rightarrow \infty).\end{equation*} Now it can be shown easily that conditions (A2) and (H) are equivalent in the case of an $m$-dependent sequence satisfying (A1) and (A3). Therefore, a formulation relevant to assumptions (A) is THEOREM 1.1 (Hoeffding-Robbins). If $\{ X_i\}$ is an $m$-dependent sequence satisfying assumptions (A), then it has the central limit property. In the case of a weakly stationary (with mean zero, say) $m$-dependent sequence, the assumptions of the theorem are satisfied except for (A3), which then is a mild additional restriction. For applications in which the existence of moments is not presupposed, e.g., strictly stationary sequences, Theorem 1.1 has been extended by Diananda [6], [7], [8] and Orey [16] in a series of results reducing the moment requirements while retaining the assumption of $m$-dependence. In the present paper the interest is in extensions relaxing the $m$-dependence assumption. A result of Ibragimov [12] in this regard implies THEOREM 1.2 (Ibragimov). If $\{ X_i\}$ is a strictly stationary sequence satisfying assumptions (A) and regularity condition (I), then it has the central limit property. (Condition (I) is defined in Section 2.) Other extensions under condition (I) but not involving stationarity assumptions are Corollary 4.1.3 and Theorem 7.2 below. See also Rosenblatt [17]. Other extensions for strictly stationary sequences, further reducing the dependence restrictions, appear in [12] and [13] and Sections 5 and 6 below. Section 2 is devoted to dependence restrictions. The restrictions (2.1), (2.2) and (2.3), later utilized in Theorem 4.1, are introduced and shown to be closely related to assumptions (A). Although conditional expectations are involved in (2.2) and (2.3), the restrictions are easily interpreted. It is found, under assumptions (A), that if (2.3) is sufficiently stringent, then (2.1) holds in a stringent form (Theorem 2.1). A link between regularity assumptions formulated in terms of joint probability distributions and those involving conditional expectations is established by Theorem 2.2 and corollaries. Implications of condition (I) are given in Theorem 2.3. Section 3 is devoted to the particular dependence restriction (2.1). Theorem 3.1 gives, under assumptions (A), a condition necessary and sufficient for (2.1) to hold in the most stringent form, (3.1). The remaining sections deal largely with central limit theorems. Section 4 obtains the basic result and its general implications. Sections 5, 6 and 7 exhibit particular results for weakly stationary sequences, sequences of martingale differences and bounded sequences. NOTATION AND CONVENTIONS. We shall denote by $\{ X_i\}^\infty_{-\infty}$ a sequence of rv's defined on a probability space. Let $\mathscr{M}_a ^b$ denote the $\sigma$-algebra generated by events of the form $\{(X_{i_1},\cdots, X_{i_k}) \varepsilon E\}$, where $a - 1 < i_1 < \cdots < i_k < b + 1$ and $E$ is a $k$-dimensional Borel set. We shall denote by $\mathscr{P}_a$ the $\sigma$-algebra $\mathscr{M}^a_{-\infty}$ of "past" events, i.e., generated by the rv's $\{ X_a, X_{a-1},\cdots\}$. Conditional expectation given a subfield $\mathscr{B}$ will be represented by $E(\cdot\mid\mathscr{B}),$ which is to be regarded as a function measurable ($\mathscr{B}$). All expectations will be assumed finite whenever expressed.

1. The Report draws together insights gained from an examination of specialist views on the application of Health and Usage Monitoring Systems (HUMS) to militaty helicopters. These views were conveyed in discussions or correspondence with the author or in published works. Special attention is given to the views expressed by various manufacturers and military operators in the USA and the UK. 2. Multi-function systems now coming into service in some civil helicopters combine the functions of accident data recording and HUMS using common equipment. Similar systems are on order by some military operators and are being evaluated by others. 3. HUMS health monitoring technologies for the transmission and engine systems are fairly mature, and selected technologies are incorporated in current commercial HUMS. Rotor track and balance is also well handled in these HUMS but diagnosis of other rotor system faults has been identified as an area requiring much more research and development The verification of health diagnostics and the development of a suitable means of interfacing with militaty aircraft maintainers continue to be health monitoring areas requiring much more attention. 4. HUMS usage monitoring has received far less attention than health monitoring. This appears to have occurred because the main emphasis to this time, for civil helicopters, has been on airworthiness aspects rather than cost benefits. Usage monitoring in currently available HUMS is limited to exceedance monitoring. U sage monitoring appears to be regarded as being more important for militaty than for civil operators, probably because there is a perception that, in general, militaty operations are more severe and more difficult to quantify than civil operations. 5. Military operators see great airworthiness benefit from health and usage monitoring techniques which provide warnings of impending failures and ensure that fatigue life-limited components are replaced before the risk of failure becomes unacceptable, but consider the fitting of HUMS can only be justified if quantifiable cost benefits can be demonstrated. 6. A major concern of militaty operators is that HUMS will become a large generator of data requiring an unacceptably high level of ground support. The development and implementation of improved infonnation management strategies which address the specific requirements of the militaty environment are considered to be essential. The use of advanced infonnation management methods, such as artificial intelligence techniques, is being actively pursued by some leading HUMS developers. 7. Research currently being undertaken on the synthesis of loads on rotating components from loads measured in the static system, may overcome some of the major concerns relating to the practicality of measuring important structural loads in the operational environment The synthesis technique provides significant scope to place load sensors in benign locations and to minimise the number of sensors required. Developments in this area are likely to influence the technologies adopted for HUMS structural usage monitoring in the longer term. 8. A number of military working groups have been set up to investigate effectiveness or implementation issues for HUMS and accident data recorders. 9. Collaborative arrangements have been established under The Technical Cooperation Program, in the area of effectiveness of HUMS in the military environment. The application of HUMS for military helicopters is lagging that for civil helicopters, but military operators are seriously examining the effectiveness of such systems for their fleets. The material presented in this document is based mainly on the author's recent discussions with researchers, manufacturers and military operators. It outlines some of the important issues which operators face and some initiatives in the area. RAAF (DTA)

Helicopter components whose fatigue lives are limited have prescribed Component Retirement Times (CRTs) that define the safe number of flying hours that they can remain in service. At the time a fleet of helicopters first enters service with a particular operator the CRTs are set by the manufacturer based on an assumed usage spectrum that has been defined with the agreement of the operator. The relationship between component loads and the various flight regimes that make up the usage spectrum is usually obtained via a flight load survey on the prototype helicopter. The Australian Defence Force discards components when they have reached their CRT. However, most components are, in effect, retired prematurely, due to the conservative nature of an assumed usage spectrum. At the other extreme, it is possible that some components could exceed their safe fatigue limit before reaching their CRT. The accurate determination of a loading history for dynamic components would have the potential to meet the two major objectives of reducing costs and improving safety. We review the literature for models that use fixed-component loads and flight parameters to model the loads in dynamics components. The reviewed papers naturally belong in one of three categories depending on model inputs: fixed-component loads, flight parameters, or a combination of fixed-component loads and flight parameters. A review of load variability reveals that even for the same aircraft under the same flight condition, the loading can vary dramatically due to pilot technique, altitude, and weight to name a few variables. For this reason, although the use of regime recognition models fleet-wide to obtain an estimate of the life fractions expended during flight on individual helicopters can produce results that are superior to the adoption of fixed CRTs, simply recognising the regime and its duration is insufficient to determine the true fraction of life expended for a component. A technique that develops a calibration matrix in the frequency domain, termed holometrics, appears promising. The holometrics technique was initially developed using only fixedcomponent loads, but was later extended to include flight parameters. Statistical methods such as significance tests and confidence intervals allow different modelling options to be prioritised. Neural network (NN) and multiple regression models were also extensively utilised by researchers. NNs were more computationally intensive than the regression models, but the NNs had better generalisation capabilities. Most studies focused on high load manoeuvres (since these produce the majority of the fatigue damage), and thus used filtering or data weighting to produce a high load bias. Adding the product of certain input parameters, such as swashplate servo position and accelerations also improved results significantly. Expert NN systems appear to be a promising area for further research. Fundamental loads modelling effects such as noise, rank deficiency, stability, and generalisation received no attention by most researchers. These essential questions need to be addressed if robust and accurate load estimation models are to be developed and implemented. A review of the literature for models that use fixed-component loads and flight parameters to determine loads in a dynamic component is presented. The reviewed papers naturally divide into one of three categories depending on the information they use to determine the load in the dynamic component. An initial section on load variability demonstrates that even for the same aircraft under the same flight condition, the loading can vary dramatically due to pilot technique, altitude, and weight to name a few variables. Neural networks, regression, and statistical indicators prove invaluable in developing load models. The review also demonstrated a lack of solutions to fundamental questions concerning loads modelling. DSTO

This is an update of, and a supplement to, the author’s earlier survey paper [18] on basic properties of strong mixing conditions. That paper appeared in 1986 in a book containing survey papers on various types of dependence conditions and the limit theory under them. The survey here will include part (but not all) of the material in [18], and will also describe some relevant material that was not in that paper, especially some new discoveries and developments that have occurred since that paper was published. (Much of the new material described here involves “interlaced ” strong mixing conditions, in which the index sets are not restricted to “past ” and “future.”) At various places in this survey, open problems will be posed. There is a large literature on basic properties of strong mixing conditions. A survey such as this cannot do full justice to it. Here are a few references on important topics not covered in this survey. For the approximation of mixing sequences by martingale differences, see e.g. the book by Hall and Heyde [80]. For the direct approximation of mixing random variables by independent ones

Helicopter Fatigue Load and Life Determination Methods

- Ryanj
- Berensa
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Aeronautical Design Standard Handbook: Condition Based Maintenance System for US Army Aircraft

- Anon

Anon., "Aeronautical Design Standard Handbook: Condition Based
Maintenance System for US Army Aircraft," US Army, ADS-79D-HDBK, Washington, D.C., March 2019.

Helicopter Rotor Loads Prediction

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An Approach to Fatigue Damage Estimation of Helicopter Rotating Components Using Computational Intelligence Techniques

- C Cheung
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Cheung, C., Rocha, B., Valdés, J. J., Kotwicz-Herniczek, M., and Li, M.,
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Components Using Computational Intelligence Techniques," Proceedings of the American Helicopter Society 69th Annual Forum, American
Helicopter Soc., May 2013.

Expanded Fatigue Damage and Load Time Signal Estimation for Dynamic Helicopter Components Using Computational Intelligence Techniques

- C Cheung
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- M Kotwicz-Herniczek

Cheung, C., Rocha, B., Valdés, J. J., Kotwicz-Herniczek, M., and
Stefani, A., "Expanded Fatigue Damage and Load Time Signal Estimation for Dynamic Helicopter Components Using Computational Intelligence Techniques," Proceedings of the American Helicopter Society
70th Annual Forum, American Helicopter Soc., May 2014.

The Health and Usage Monitoring of Helicopter Systems-The Next Generation

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Roe, J. D., and Astridge, D. G., "The Health and Usage Monitoring of
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Leveraging Digital Clones for Prognostics Health Management

- A P Vechart
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- J Szpylman

Vechart, A. P., Rios, J., McReynolds, M., and Szpylman, J., "Leveraging
Digital Clones for Prognostics Health Management," 11th Defence
Science and Technology (DST) International Conference on Health
and Usage Monitoring (HUMS 2019), Engineers Australia, Royal
Aeronautical Soc., Melbourne, Australia, 2019, pp. 910-915.

Sikorsky Aircraft Division, AGARD CP-122

- P Arcidiacono
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Arcidiacono, P., and Carlson, R., "Helicopter Rotor Loads Prediction,"
Sikorsky Aircraft Division, AGARD CP-122, 1973, pp. 4-1, 4-12.