A method for detecting faults in integrated navigation system based on improved SPRT adaptive filtering

A non-parametric sequential rank-sum probability ratio test method for binary hypothesis testing

The real-time fault detection and diagnosis algorithm of a liquid rocket engine is the basis of online reconfiguration of guidance and the control system of a launch vehicle, which is directly related to the success or failure of space mission. Based on previous related works, this paper carries out comparative experimental studies of relevant intelligent algorithm models for real-time fault detection engineering application requirements of a liquid hydrogen–oxygen rocket engine. Firstly, the working state and detection parameters’ selection of a hydrogen–oxygen engine are analyzed, and the proposed three real-time intelligent fault detection algorithm model design methods are elaborated again. Fault detection calculation and analysis are carried out through normal test data and fault test data. The comparative analysis results of real-time intelligent fault detection algorithm models is presented from three dimensions: detection time, fault detection, and stability and consistency. Finally, based on a correlation analysis, a comprehensive intelligent fault diagnosis model design framework is given to further solve the requirements of real-time fault detection and diagnosis engineering development of a liquid rocket engine, a complex piece of equipment.

Because computers (except for parallel computers) generate simulation outputs sequentially, we recommend sequential probability ratio tests (SPRTs) for the statistical analysis of these outputs. However, until now simulation analysts have ignored SPRTs. To change this situation, we review SPRTs for the simplest case; namely, the case of choosing between two hypothesized values for the mean simulation output. For this case, the classic SPRT of Wald (Wald A. Sequential tests of statistical hypotheses. Ann Math Stat 1945; 16: 117–186) allows general types of distribution, including normal distributions with known variances. A modification permits unknown variances that are estimated. Hall (Hall WJ. Some sequential analogs of Stein’s two-stage test. Biometrika 1962; 49: 367–378) developed a SPRT that assumes normal distributions with unknown variances estimated from a pilot sample. A modification uses a fully sequential variance estimator. In this paper, we quantify the performance of the various SPRTs, using several Monte Carlo experiments. In experiment #1, simulation outputs are normal. Whereas Wald’s SPRT with estimated variance gives too high error rates, Hall’s original and modified SPRTs are “conservative”; that is, the actual error rates are smaller than those prespecified (nominal). Furthermore, our experiment shows that the most efficient SPRT is Hall’s modified SPRT. In experiment #2, we estimate the robustness of these SPRTs for non-normal output. For these two experiments, we provide details on their design and analysis; these details may also be useful for simulation experiments in general.

In medical, health, and sports sciences, researchers desire a device with high reliability and validity. This article focuses on reliability and validity studies with n subjects and m ≥2 repeated measurements per subject. High statistical power can be achieved by increasing n or m, and increasing m is often easier than increasing n in practice unless m is too high to result in systematic bias. The sequential probability ratio test (SPRT) is a useful statistical method which can conclude a null hypothesis H0 or an alternative hypothesis H1 with 50% of the required sample size of a non-sequential test on average. The traditional SPRT requires the likelihood function for each observed random variable, and it can be a practical burden for evaluating the likelihood ratio after each observation of a subject. Instead, m observed random variables per subject can be transformed into a test statistic which has a known sampling distribution under H0 and under H1. This allows us to formulate a SPRT based on a sequence of test statistics. In this article, three types of study are considered: reliabilityof a device, reliability of a device relative to a criterion device, and validity of a device relative to a  criterion device. Using SPRT for testing the reliability of a device, for small m, results in an average sample size of about 50% of the fixed sample size for a non-sequential test. For comparing a device to criterion, the average sample size approaches to 60% approximately as m increases. The SPRT tolerates violation of normality assumption for validity study, but it does not for reliability study.

We consider a single-hop, random-access, wireless sensor network (WSN) performing sequential distributed detection under a bandwidth constraint. At each time slot, the sensor nodes will make their decisions on whether the observed event is happening. The sensor censoring strategy is applied such that only the local decisions equal to one (i.e., the event happens) will be sent to the fusion center (FC). Because only one transmission channel between the FC and the sensor nodes is assumed, if two or more local decisions are sent at a time slot, a packet collision happens. We design a sequential probability ratio test (SPRT) at the FC that is aware of the collisions. The performance measures of the collision-aware SPRT are analyzed based on a Markov chain. In addition, we derive the asymptotic relative efficiency of the collision-aware SPRT relative to another SPRT. Numerical results show some interesting characteristics of the collision-aware SPRT. For example, the collision-aware SPRT prefers the scenario that many local decisions are likely to be sent per time slot.

Robust UKF orbit determination method with time-varying forgetting factor for angle/range-based integrated navigation system

Celestial navigation system (CNS) is a completely autonomous navigation technology with strong anti-interference ability and high navigation accuracy, which has a great application prospect. Aim at defect of traditional integrated navigation system using attitude angle measurement celestial navigation system and strapdown inertial navigation system (SINS), which can only correct of strapdown inertial navigation system’s gyro drift. This paper proposes an improved integrated navigation system that add double-star positioning celestial navigation to traditional SINS/CNS integrated navigation system, meanwhile, introduces the fault detection technology based on statistical distance to solve the problem that inaccuracy of measurement information leads to the integrated navigation system’s performance degradation. By analyzing the simulation results, the improved navigation system can inhibit divergence of system and obtain high accurate and stable navigation information.

Using one class SVM to counter intelligent attacks against an SPRT defense mechanism

Testability plays an important role in the readiness of equipment as a good design for testability (DFT) can greatly decrease the fault detection and isolation time, which will accelerate the maintenance actions. Testability verification is a procedure to check that whether the testability indexes such as fault detection rate (FDR) and fault isolation rate (FIR) meet the requirement in the contract. Currently, standards and statistical methods used in testability verification have the problems such as large sample, long period and so on. Sequential probability ratio test (SPRT) method can decrease the test sample size with almost a same operation characteristic as classical method based on binomial distribution. SPRT method and its truncated rules are introduced and the spectrum of expected test number is proposed. Then, the sample size allocation method and failure mode selection method based on failure rate used in sequential testability verification are illustrated. Testability verification of a control system is implemented with the given method and steps. Software named testability demonstration and evaluation system (TDES) which can calculate the decision criteria, plot decision chart, select failure mode and make judgment is used in the test as assistance. The result shows that the test sample size is remarkably decreased while comparing with the classical method.

The sequential probability ratio test (SPRT) is a fundamental tool for sequential analysis. It forms the basis of numerous sequential techniques for different applications; for example, the truncated SPRT and Page's cumulative sum test (CUSUM). The performance of SPRT is characterized by two important functions—operating characteristic (OC) and average sample number (ASN), and CUSUM's performance is revealed by the average run length (ARL) function. These functions have been studied extensively under the assumption of independent and identically distributed log-likelihood ratios (LLRs) with constant bounds, which is too stringent for many applications. In this article, inductive integral equations governing these functions are developed under very general settings—the bounds can be time-varying and the LLRs are assumed independent but nonstationary. These inductive equations provide a theoretical foundation for performance analysis. Unfortunately, they have nonunique solutions in the general case except for the truncated SPRT. Numerical solutions for some frequently encountered special cases are developed and are compared with the results of Monte Carlo simulations.

In this article the problem of a sequential test for the model of independent non-identically distributed observations is considered. Based on recursive calculation a new numerical approach to approximate test characteristics for a sequential probability ratio test (SPRT) and a truncated SPRT (TSPRT) is constructed. The problem of robustness evaluation is also studied when the contamination is presented by the distortion of the distributions of all increments of the log-likelihood ratio statistics. The two-side truncated functions are proposed to be used for constructing the robustified SPRT. An algorithm to choose the thresholds of these truncated functions is indicated. The results are applied for a sequential test on parameters of time series with trend. Some kinds of the contaminated models of time series with trend are used to study the robustness of the truncated SPRT. Numerical examples confirming the theoretical results mentioned above are given.

Fault Detection in Multiply-Redundant Measurement Systems

The monitor of lithium-ion battery health is becoming a challenge because the performance of battery is effect by many environment factors. To address this problem, a new health monitor method based on Multivariate State Estimation Technique (MSET) and Sequential Probability Ratio Test (SPRT) is proposed in this paper. In order to demonstrate the performance gain of the method, a detailed experiment is performed based on a lithium-ion battery. By the comparison of performance parameters actual residuals and healthy residuals driven from the training data based on MSET, the fault detection can be implemented based on the SPRT.

We apply high-dimensional analysis of variance (HANOVA) and sequential probability ratio test (SPRT) to detect buried land mines from array ground penetrating radar (GPR) measurements. The GPR array surveys a region of interest in a progressive manner starting at a known position and moving step by step in a fixed direction. Our detection method consists of two stages. Because, at each stop of the array the path lengths are different from every transmitter/receiver pair to a mien target, there exists statistically significant difference among received signals when a mine target is presented. Thus, the first step in our processing consists of a HANOVA test to detect this statistical difference at each stop. HANOVA does not incorporate new data as the GPR array moves down-track. So secondly, we resort to a sequential probability ratio test to look for changes in the HANOVA statistics as the array proceeds down track. The SPRT allows for real-time processing as anew data are obtained by the GPR array. Finally, real sensor data are processed to verify the method.

The SPRT control chart for the process mean with samples starting at fixed times